Thermal Properties of Matter Test

Result

Thermal Properties of Matter Test - 72

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Weekly Quiz Competition

Question 1
1 / -0

With rise in temperature, density of a given body change according to one of the following relations

A
$$\rho = \rho_0 [1+\gamma d \theta]$$

B
$$\rho = \rho_0 [1-\gamma d \theta]$$

C
$$\rho = \rho_0 \gamma d \theta$$

D
$$\rho = \rho_0 /\gamma d \theta$$

Solution
Question 2
1 / -0

The figure shows a system of two thin concentric spherical shells of radii $${r_1}\;{\text{and}}\;{r_2}$$ and kept at temperatures $${T_1}\;{\text{and}}\;{T_2}$$ respectively. The radial rate of heat in a substance between the two concentric spheres is proportional to :

A
$$\dfrac{{{r_1}{r_2}}}{{\left( {{r_2} - {r_1}} \right)}}$$

B
$${\left( {{r_2} - {r_1}} \right)}$$

C
$$\dfrac{{\left( {{r_2} - {r_1}} \right)}}{{{r_1}{r_2}}}$$

D
$$\log \left( {\dfrac{{{r_2}}}{{{r_1}}}} \right)$$
Question 3
1 / -0

Critical temperature of a gas obeying van der waals' equation is :

A
$$\dfrac{8a}{27Rb}$$

B
$$\dfrac{a}{27b^2r}$$

C
$$3b$$

D
$$\dfrac{1}{27Rb}$$

Solution
Question 4
1 / -0

Which of the following does not affect the distribution of insolation?

A
Altitude

B
Angle of sun's rays

C
Length of the day

D
Ocean currents
Question 5
1 / -0

Two materials having coefficients of thermal conductivity $$'3K'$$ and $$'K'$$ and thickness 'd' and $$'3d'$$, respectively, are joined to form a slab as shown in the figure. The temperature of the outer surfaces are $$'\theta_2'$$ and $$'\theta_1'$$ respectively, $$(\theta_2 > \theta_1)$$. The temperature at the interface is?

A
$$\dfrac{\theta_2+\theta_1}{2}$$

B
$$\dfrac{\theta_1}{10}+\dfrac{9\theta_2}{10}$$

C
$$\dfrac{\theta_1}{3}+\dfrac{2\theta_2}{3}$$

D
$$\dfrac{\theta_1}{6}+\dfrac{5\theta_2}{6}$$

Solution

Let the temperature of interface be $$"\theta"$$
$$i_1=i_2$$$$\{$$ Steady state conduction$$\}$$
$$\dfrac{ 3KA(\theta_2-\theta)}{d}=\dfrac{KA(\theta -\theta_1)}{3d}$$
$$9\theta_2 - 9\theta =\theta - \theta_1$$
$$9\theta_2+\theta_1=\theta +9\theta$$
$$\theta =\dfrac{9\theta_2}{10}+\dfrac{\theta_1}{10}$$.
Question 6
1 / -0

In a Carnot engine, when heat is absorbed from the source, temperature of source

A
Increases

B
Decreases

C
Remains constant

D
Cannot say

Solution
Question 7
1 / -0

At ordinary temperature,the molecule of an ideal gas have only translation and rotational kinetic energies. At high temperature,they may have vibrational energy.As a result of this, at higher temperature molar specific heat capacity at constant volume $$ C_v $$ for a diatomic gas is

A
$$ = \frac {5R}{2} $$

B
$$ < \frac {5R}{2} $$

C
$$ > \frac {3R}{2} $$

D
$$ = \frac {3R}{2} $$
Question 8
1 / -0

One mole of an ideal gas passes through a process where pressure and volume obey the relation $$P = P_0 \left[1 - \dfrac{1}{2} \left(\dfrac{V_0}{V} \right)^2 \right]$$. Here $$P_0$$ and $$V_0$$ are constants . Calculate the change in the temperature of the gas if its volume change from $$V_o $$ to $$2 V_o$$.

A
$$\dfrac{1}{2} \dfrac{P_o V_o}{R}$$

B
$$\dfrac{3}{4} \dfrac{P_o V_o}{R}$$

C
$$ \dfrac{5}{4} \dfrac{P_o V_o}{R}$$

D
$$\dfrac{1}{4} \dfrac{P_oV_o}{R}$$

Solution
Question 9
1 / -0

A compound rod is formed of a steel core of diameter $$1cm$$ and outer casing is of copper, whose outer diameter is $$2 cm$$. The length of this compound rod is $$2m$$ and one end is maintained as $$100^{\circ}C$$, and the end is at $$0^{\circ}C$$. If the outer surface of the rod is thermally insulated, then heat current in the rod will be:
(Given : Thermal conductivity of steel $$= 12\ cal/m-K-s$$, thermal conductivity of copper $$= 92\ cal/m-K-s$$).

A
$$2\ cal/s$$

B
$$1.13\ cal/s$$

C
$$1.42\ cal/s$$

D
$$2.68\ cal/s$$

Solution
Question 10
1 / -0

Five wires each of cross-sectional area A and length l are combined as shown in figure. The thermal conductivity of copper and steel are K1 and K2 respectively. If $$A$$ is maintained at $$100^{\circ}C$$ and $$C$$ is maintained at $$0^{\circ}C$$. The rate emitted at $$C$$ is : (assume the curve surfaces of rods are thermally insulated).

A
$$\dfrac {50A(K_{1} + K_{2})}{l}$$

B
$$\dfrac {100A(K_{1} + K_{2})}{l}$$

C
$$\dfrac {A(K_{1} + K_{2})}{l}$$

D
None of these

Solution