Thermal Properties of Matter Test

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Thermal Properties of Matter Test - 50

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Question 1
1 / -0

The velocities of sound in an ideal gas at temperature $$T_1$$ and $$T_2 k$$ are found to be $$V_1$$ and $$V_2$$ respectively.If the r.m.s. velocities of the molecules of the same gas at the same temperatures $$T_1$$ and $$T_2$$ are $$v_1$$ and $$v_2$$ respectively then

A
$$v_2=v_1(\dfrac{V_1}{V_2})$$

B
$$v_2=v_1(\dfrac{V_2}{V_1})$$

C
$$v_2=v_1\sqrt{\dfrac{V_2}{V_1}}$$

D
$$v_2=v_1\sqrt{\dfrac{V_1}{V_2}}$$

Solution
Question 2
1 / -0

A certain perfect gas occupying $$1\ litre$$ at $$80\ cm$$ of Hg, suddenly expands to $$1190\ cc$$, while the pressure falls to $$60\ cm$$ of Hg. Therefore, the gas is ?

A
polyatomic

B
diatomic

C
monoatomic

D
data inadequate

Solution
Question 3
1 / -0

Find the temperature of the junction shown in the figure for three rods; identical in dimensions:

A
$$40^0C$$

B
$$60^0C$$

C
$$30^0C$$

D
$$80^0C$$

Solution
Question 4
1 / -0

A laboratory thermometer gave the reading of $$-1^oC$$ and $$99^o C$$ when inserted into melting ice and boiling water respectively, both at standard atmospheric pressure. What is the error when the same thermometer is used to measure the difference between two arbitrary temperatures?

A
$$-1^o C$$

B
$$1^o C$$

C
$$0^o C$$

D
$$2^o C$$
Question 5
1 / -0

The figure shows a glass tube (linear coefficient of expansion is $$\sigma$$) completely filled with a liquid of volume expansion coefficient $$\gamma$$. On heating, length of the liquid column does not change. Choose the correct relation between $$\gamma$$ and $$\sigma$$.

A
$$\gamma = \alpha$$

B
$$\gamma =2 \alpha$$

C
$$\gamma = 3\alpha$$

D
$$\gamma = \alpha/3$$

Solution

When length of liquid coloumn remains constant,
then the level of liquid moves down w.r.t container
thus $$\gamma=3\alpha$$
Now, $$V=V_o(1+\gamma^{\Delta T})$$
Since, $$V=Al_o=[A_o(1+2\alpha \Delta T)]10=V_o(1+2\alpha \Delta t)$$
Hence, $$V_o(1+\gamma^{\Delta T})=V_o(1+2 \alpha \Delta T)$$
$$\Rightarrow \gamma= 2 \alpha$$
Question 6
1 / -0

Three identical iron rods are welded together to form the shape of $$Y$$. The top ends of the $$Y$$ are maintained at $$0^{o}C$$ and the bottom ends is maintained at $$60^{o}C$$. The temperature of the junction of the three rods is

A
$$10^{o}\ C$$

B
$$20^{o}\ C$$

C
$$25^{o}\ C$$

D
$$40^{o}\ C$$

Solution
Question 7
1 / -0

A flask contains $$100$$ $$c ^ { 2 }$$ of a liquid at $$10 ^ { \circ } \mathrm { C }$$ When it is heated to $$110 ^ { \circ } C$$ increase in volume of the liquid appears to be $$2$$ $$c c$$ Find the coefficient of real expansion of the liquid.$$\left( \alpha \text { of flask is } 11 \times 10 ^ { - 6 } / ^ { 0 } \mathrm { C } \right)$$

A
$$2.33 \times 10 ^ { - 4 } / ^ { 0 } \mathrm { C }$$

B
$$3.33 \times 10 ^ { - 10 } \mathrm { C }$$

C
$$23.3 \times 10 ^ { - 4 } / ^ { 0 } \mathrm { C }$$

D
$$33.3 \times 10 ^ { - 1 } \mathrm { CC }$$

Solution
Question 8
1 / -0

Two new thermometer scales X and Y are plotted as shown. The LFP and UFP of Y-scale are $$0^{\circ}$$ and $$90^{\circ}$$ respectively. Then the corresponding values on X-scale are

A
$$-10^{\circ}$$, $$100^{\circ}$$

B
$$0^{\circ}$$, $$80^{\circ}$$

C
$$10^{\circ}$$, $$90^{\circ}$$

D
$$10^{\circ}$$, $$100^{\circ}$$

Solution

$$\textbf{Given}:$$ LFP of the thermometer Y is $$0^o$$, UFP of the thermometer Y is $$100^0$$

$$\textbf{Solution}:$$
Let us find the graph equation now, It is a straight line, so the equation will be of form y=mx+c.
The slope of the line is equal to m= $$tan 45^0$$, m = 1
The constant is the y coordinate when x is equal to 0.
Therefore, c=-10.
Now, the equation we get is,
y=x-10
Let us find the LFP of the thermometer X as Value of Y is given.,
y=mx+c
$$\implies 0=x-10$$
$$\implies x=10^0$$
$$\therefore$$, the LFP of the thermometer X is 10 degrees.

Now, the UFP of the thermometer X can be founds similarly as,
y=x-10
$$\implies 90=x-10$$
$$\implies x=100^0$$
Hence, the UFP of the thermometer X is 100 degrees.

$$\textbf{Hence D is the correct option}$$
Question 9
1 / -0

Two moles of an ideal gas X occupying a volume V excert a pressure P. The same pressure is excert by one mole of another gas Y occupying a volume 2V. (if the molecular weight of Y is 16 times the molecular weight of X), find the ratio of the 'rms' speed of the molecular of X and Y.

A
$$2$$

B
$$4$$

C
$$\frac { 1 }{ 2 } $$

D
$$\sqrt { 2 } $$

Solution

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Question 10
1 / -0

The temperature of a diatomic gas is T. The total kinetic energy of the gas is given as $$E = { K }_{ 1 }$$ where $${ K }_{ 1 }$$ is constant. Find out the total number of molecules of the gas in the sample. (K = Boltzaman's constant)

A
$$3K_{ 1 }K$$

B
$$5K_{ 1 }/2K$$

C
$$2K_{ 1 }/5K$$

D
None of these

Solution