Thermal Properties of Matter Test

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Thermal Properties of Matter Test - 73

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Question 1
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If the thermal conductivity of the material of the rod of length $$l$$, is $$K$$, then the rate of heat flow through a tapering rod, tapering from radius $$r_{1}$$ and $$r_{2}$$, if the temperature of the ends are maintained at $$T_{1}$$ and $$T_{2}$$, is

A
$$\dfrac {\pi Kr_{1}r_{2}(T_{1} + T_{2})}{l}$$

B
$$\dfrac {\pi Kr_{1}r_{2}(T_{1} - T_{2})}{l}$$

C
$$\dfrac {\pi Kr_{1}r_{2}(T_{1} - T_{2})}{2l}$$

D
$$\dfrac {\pi Kr_{1}^{2}(T_{1} + T_{2})}{l}$$

Solution
Question 2
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The ice is filled in a hollow glass sphere of thickness $$2\ mm$$ and external radius $$10\ cm$$. This hollow glass sphere with ice now placed in a bath containing boiling water at $$100^{\circ}C$$. The rate at which ice melts, is: (Neglect volume change in ice)
(Given : thermal conductivity of glass $$1.1\ W/m/K$$, latent heat of ice $$= 336\times 10^{3} J/kg$$).

A
$$\dfrac {m}{t} = 0.01\ kg/s$$

B
$$\dfrac {m}{t} = 0.002\ kg/s$$

C
$$\dfrac {m}{t} = 0.02\ kg/s$$

D
$$\dfrac {m}{t} = 0.001\ kg/s$$

Solution
Question 3
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A block of ice at $$0^{\circ}$$ rests on the upper surface of the slab of stone of area $$3600\ cm^{2}$$ and thickness of $$10\ cm$$. The slab is exposed on the lower surface to steam at $$100^{\circ}C$$. If $$4800\ g$$ of ice is melted in one hour, then the thermal conductivity of stone is:
(Given: The latent heat of fusion of ice $$= 80\ cal/gm)$$.

A
$$K = 2.96\times 10^{-3} cal/ cm\ s^{\circ}C$$

B
$$K = 1.96\times 10^{-3} cal/ cm\ s^{\circ}C$$

C
$$K = 0.96\times 10^{-3} cal/ cm\ s^{\circ}C$$

D
None of the above

Solution
Question 4
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The value of $$ C_p - C_v $$ is 1:00 R for a gas sample in state A and is 1.08 R in state B. Let $$ P_A, P_a $$ denote the pressures and $$ T_A\ and\ T_a $$ denote the temperature of the states $$A$$ and $$a$$ respectively.Most likely

A
$$ P_A < P_a\ and\ T_A > T_e $$

B
$$ P_A > P_a\ and\ T_A < T_a $$

C
$$ P_A = P_a\ and\ T_A < T_a $$

D
$$ p_A > P_a\ and\ T_A = T_e $$

Solution
Question 5
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Directions For Questions

A thin copper rod of uniform cross-section $$A$$ square meters and of length $$L$$ meters has a spherical metal sphere of radius $$r \ m$$ at its one end symmetrically attached to the copper rod. The thermal conductivity of copper is $$K$$ and the emissivity of the spherical surface of the sphere is $$\varepsilon$$. The free and of the copper rod is maintained at the temperature $$T$$ kelvin by supplying thermal energy from a $$P$$ watt source. Steady-state conditions are allowed to be established while the rod is properly insulated against heat loss from the sides. Surrounding are at $$0^{o}C$$. Stefan's constant $$=\sigma W/\ m^{2}K^{4}$$:

...view full instructions

If the metal sphere attached at the end of the copper rod is made of brass, whose thermal conductivity is $$K_{b}<K$$, then which of the following statements is true?

A
The temperature of the sphere will, under steady state conditions, continue to be $$T_{B}$$

B
The power that will be radiated out from the sphere will still be $$P_{S}$$

C
It will take smaller time for steady state conditions to be reaches

D
The rate of thermal energy transmitted across the copper rod, under steady state, will be reduced

Solution
Question 6
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A heater of constant power is used to boil water in a pot. During heating, temperature of water increases from $$ 60^o C$$ to $$65^o C $$ in $$1.0 \ min$$. When the heater is switched off, temperature of water falls from $$ 65^o C$$ to $$60^o C $$ in $$9.0 \ min$$. If rate of heat dissipation to the surrounding remains almost constant, what proportion of heat received by water during heating would be dissipated to the surroundings?

A
$$9\%$$

B
$$10\%$$

C
$$12.5\%$$

D
$$15\%$$

Solution
Question 7
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Directions For Questions

A thin copper rod of uniform cross section $$A$$ square meters and of length $$L$$ meters has a spherical metal sphere of radius $$r \ m$$ at its one end symmetrically attached to the copper rod. The thermal conductivity of copper is $$K$$ and the emissivity of the spherical surface of the sphere is $$\varepsilon$$. The free and of the copper rod is maintained at the temperature $$T$$ kelvin by supplying thermal energy from a $$P$$ watt source. Steady state conditions are allowed to be established while the rod is property insulated against heat loss from the sides. Surrounding are at $$0^{o}C$$. Stefan's constant $$=\sigma W/\ m^{2}K^{4}$$:

...view full instructions

After the steady state conditions are reached, the temperature of the spherical end of the rod, $$T_{S}$$ is:

A
$$T_{S}=T-\dfrac{P(L+r)}{KA}$$

B
$$T_{S}=0^{o}C$$

C
$$T_{S}=\dfrac{PL}{KA}$$

D
$$T_{S}=T-\dfrac{PL}{KA}$$

Solution

The distance from the end A of the copper rod (where power is supplied) and centre O of the metal sphere is (L+r). Hence , in the steady state condions,
$$P$$=$$\dfrac{KA(T−T_{S})}{L+r}$$
Which gives $$T_{S}=T-\dfrac{P(L+r)}{KA}$$
(The heat is trainsmitted up to centre of the spherical end and the sphere loses energy by radiation out of its spherical surface.)
Question 8
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Directions For Questions

A thin copper rod of uniform cross section $$A$$ square meters and of length $$L$$ meters has a spherical metal sphere of radius $$r \ m$$ at its one end symmetrically attached to the copper rod. The thermal conductivity of copper is $$K$$ and the emissivity of the spherical surface of the sphere is $$\varepsilon$$. The free and of the copper rod is maintained at the temperature $$T$$ kelvin by supplying thermal energy from a $$P$$ watt source. Steady state conditions are allowed to be established while the rod is property insulated against heat loss from the sides. Surrounding are at $$0^{o}C$$. Stefan's constant $$=\sigma W/\ m^{2}K^{4}$$:

...view full instructions

The net power that will be radiated out, $$P_{S}$$, from the sphere after steady state conditions are reached is:

A
$$P_{S}=P$$

B
$$P_{S}=\dfrac{PA}{4\pi r^{2}}$$

C
$$P_{S}=0$$

D
$$P_{S}=\sigma \varepsilon T_{5}^{4}$$

Solution

Under steady state conditions, all temperature remain constant including $$T_{S}$$, the temperature at centre of sphere. Hence no thermal energy accumulates inside the sphere. Hence $$P_{S}$$=$$P$$= energy received from source.
Question 9
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Directions For Questions

A $$500\ g$$ teapot and an insulated thermos are in a $$20^{o}C$$ room. The teapot is filled with $$1000\ g$$ of the boiling water. $$12$$ tea bags are then placed into the teapot. The brewed tea is allowed to cool to $$80^{o}C$$, then $$250\ g$$ of the tea is poured from the teapot into the thermos. The teapot us then kept on an insulated warmer that transfers $$500\ cal/min$$ to the tea. Assume that the specific heat of brewed tea is the same as that of pure water, and that the tea bags have a very small mass compared to that the water, and a negligible effect on the temperature. The specific heat of teapot is $$0.17\ J/g\ K$$ and that of water is $$4.18\ J/g\ K$$. The entire procedure is done under atmosphere pressure. There are $$4.18\ J$$ in one caloric.

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After the tea is added to the thermos, the temperature of the liquid quickly falls from $$80^{o}C$$ to $$75^{o}C$$ as $$i$$ reaches thermal equilibrium with the thermos flask
What is the heat capacity of the thermos?

A
$$9.5\ J/K$$

B
$$14\ J/K$$

C
$$95\ J/K$$

D
$$878\ J/K$$

Solution
Question 10
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Directions For Questions

A $$500\ g$$ teapot and an insulated thermos are in a $$20^{o}C$$ room. The teapot is filled with $$1000\ g$$ of the boiling water. $$12$$ tea bags are then placed into the teapot. The brewed tea is allowed to cool to $$80^{o}C$$, then $$250\ g$$ of the tea is poured from the teapot into the thermos. The teapot us then kept on an insulated warmer that transfers $$500\ cal/min$$ to the tea. Assume that the specific heat of brewed tea is the same as that of pure water, and that the tea bags have a very small mass compared to that the water, and a negligible effect on the temperature. The specific heat of teapot is $$0.17\ J/g\ K$$ and that of water is $$4.18\ J/g\ K$$. The entire procedure is done under atmosphere pressure. There are $$4.18\ J$$ in one caloric.

...view full instructions

An alternative method for keeping the tea hot would be to place the teapot on a $$10$$ pound block that has been heated in an oven to $$300^{o}C$$. A block of which of the following substance would best be able to keep the tea hot?

A
copper (specific heat $$=0.39\ J/g\ K$$)

B
granite (specific heat $$=0.79\ J /g\ K$$)

C
iron (specific heat $$=0.45\ J/g\ K$$)

D
pewter (specific heat $$=0.17\ J/g\ K$$)

Solution