Temperature

Q.

What is the relation between pressure and kinetic energy of gas?

Q.

A cylinder of radius R made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radiusRand outer radius 2Rmade of material of thermal conductivity $K_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

1. 

2. 

3. 

4. 

Q.

A mono atomic gas at a pressure p, having a volume V expands isothermally to a volume 2V and then adiabatically to a volume 16V. The final pressure of the gas is $(\gamma =\frac{5}{3})$ :

1. $64p$

2. $32p$

3. $\frac{p}{64}$

4. $16p$

Q. The temperature of a gas is raised from ${27}^{\circ }\text{C}$ to ${927}^{\circ }\text{C}$. The root mean square speed

1. remains the same.
2. gets doubled.
3. becomes $\sqrt{\frac{927}{27}}$ times the earlier value.
4. gets halved.

Q. The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to
(Take $g=10m/s^2$)

1. ${10}^4\text{K}$
2. $650\text{K}$
3. $3\times {10}^5\text{K}$
4. $800\text{K}$

Q. how will you distinguish between a hard boiled egg and a raw egg by spinning each on a table top

Q. Three rods of copper, brass and steel are welded together to form a Y - shaped structure. Area of cross - section of each rod $=4{\text{cm}}^2$. End of copper rod is maintained at ${100}^{\circ }C$ where as ends of brass and steel rods are kept at $0^{\circ }C$. Lengths of the copper, brass and steel rods are $46,13\text{and}12\text{cm}$ respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are $0.92,0.26$ and $0.12$ CGS units respectively. Rate of heat flow through copper rod is

1. $2.4\text{cal/s}$
2. $6.0\text{cal/s}$
3. $1.2\text{cal/s}$
4. $4.8\text{cal/s}$

Q.

An engine takes in $5$ moles of air at ${20}^{0}C$ and 1atm, and compresses it adiabatically to $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$10$}\right.th$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $XkJ$. The value of $X$ to the nearest integer is ______.

Q. Thermal resistance $\left(R\right)$ of a spherical shell having inner radius $r_1$ and outer radius $r_2$ is given by,
($K$ is the thermal conductivity of the shell.)

1. $R=\frac{r_1{r}_2}{4\pi K(r_2-r_1)}$
2. $R=\frac{r_2-r_1}{4\pi K\left(r_1{r}_2\right)}$
3. $R=\frac{r_1{r}_2}{4K(r_2-r_1)}$
4. $R=\frac{r_2-r_1}{4K\left(r_1{r}_2\right)}$

Q.

When the temperature of a gas is raised from ${27}^{\circ }$ C to ${90}^{\circ }$ C, the percentage increase in the r.m.s. velocity of the molecules will be

1. 10%
2. 15%
3. 20%
4. 17.5%

Q. A gas is enclosed in a closed pot. On keeping this pot in a train moving with high speed , the temperature of the gas

1. will increases
2. will decreases
3. will remain the same
4. will change according to the nature of the gas

Q. The temperature of argon, kept in a vessel is raised by $1^{\circ }C$ at a constant volume. The total heat supplied to the gas is a combination of translational and rotational energies. Their respective shares are

1. 60% and 40%
2. 40% and 60%
3. 50% and 50%
4. 100% and 0%

Q.

Is it possible to change the temperature and pressure of a fixed mass of a gas, without changing its volume?

Q.

The mean free path of molecules of a gas is inversely proportional to

1. $r^3$

2. $r^2$

3. $r$

4. $\sqrt{r}$

Q.

A small helium tank measures about two feet ($60cm$) high.

Yet it can fill over $50$balloons

How can such a small tank contain enough helium to fill so many balloons?

Q. One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where $V$ is the volume and $T$ is the temperature). Which of the statements below is (are) true?

1. Process I is an isochoric process
2. In process II, gas absorbs heat
3. In process IV, gas releases heat
4. Processes I and II are not isobaric

Q. The figure shows the face and interface temperature of a composite slab consisting of four materials, of identical thickness, through which the heat transfer is steady. Which material has minimum thermal conductivity?

1. $\text{d}$
2. $\text{a}$
3. $\text{b}$
4. $\text{c}$

Q. Eleven identical rods are arranged as shown in figure. Each rod has length $L$, cross-sectional area $A$ and thermal conductivity of material $K$. Ends A and F are maintained at temperatures $T_1$ and $T_2(T_2<T_1)$ respectively. If lateral surface of each rod is thermally insulated, the rate of heat transfer$\left(\frac{dQ}{dt}\right)$ in each rod is

1. ${\left(\frac{dQ}{dt}\right)}_{AB}={\left(\frac{dQ}{dt}\right)}_{CD}$
2. ${\left(\frac{dQ}{dt}\right)}_{BE}=\frac{2}{7}\frac{(T_1-T_2)KA}{t}$
3. ${\left(\frac{dQ}{dt}\right)}_{CH}\ne {\left(\frac{dQ}{dt}\right)}_{DG}$
4. ${\left(\frac{dQ}{dt}\right)}_{BC}={\left(\frac{dQ}{dt}\right)}_{DC}$

Q. Inner surface of a cylindrical shell of length $l$ and of material of thermal conductivity $k$ is kept at constant temperature $T_1$ and outer surface of the cylinder is kept at constant temperature $T_2$ such that $(T_1>T_2)$ as shown in figure. Heat flows from inner surface to outer surface radially outward. Inner and outer radii of the shell are $R$ and $2R$ respectively. Due to lack of space this cylinder has to be replaced by a smaller cylinder of length $\frac{l}{2}$ inner and outer radii $\frac{R}{4}$ and $R$ respectively and thermal conductivity of material $nk$. If rate of radially outward heat flow remains same for same temperatures of inner and outer surface i.e., $T_1$ and $T_2$, then find the value of $n$.

Q. Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300K$ and $T_2=100K$ as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1$ and $K_2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200K$. Then $\frac{K_1}{K_2}=$

Q.

Real gases obey gas laws under all conditions.

1. True
2. False

Q. A bar of copper of length $75\text{cm}$ and a bar of steel of length $125\text{cm}$ are joined together end to end. Both are of circular cross-section with diameter $2\text{cm}$. The free ends of the copper and the steel bars are maintained at ${100}^{\circ }\text{C}$ and $0^{\circ }\text{C}$ respectively. The curved surfaces of the bars are thermally insulated. What is the temperature of the $\text{copper - steel}$ junction?
$[\text{Take}:K_{\text{Cu}}=386{\text{Js}}^{-1}{\text{m}}^{-1}{}^{\circ }{\text{C}}^{-1}{K}_{\text{steel}}=46{\text{Js}}^{-1}{\text{m}}^{-1}{}^{\circ }{\text{C}}^{-1}]$

1. ${63}^{\circ }\text{C}$
2. ${73}^{\circ }\text{C}$
3. ${83}^{\circ }\text{C}$
4. ${93}^{\circ }\text{C}$

Q.

If the molecular weight of two gases are $M_1$ and $M_2$, then at a given tempreture the ratio of their root mean square velocity $v_1$ and $v_2$ will be

1. 

2. 

3. 

4. 

Q. Is it possible to distinguish between a raw egg and hard boiled egg by spinning each on a table? Justify your answer.

Q. A gas is enclosed in a closed pot. On keeping this pot in a train moving with high speed, the temperature of the gas

1. Will increase
2. Will decrease
3. Will remain the same
4. Will change according to the nature of the gas

Q. $\gamma$ represents the ratio of the specific heats of a gas. For a given mass of the gas, the change in internal energy when the volume expands from V to 3V at constant pressure P is:

1. $\frac{3PV}{\gamma -1}$
2. $\frac{3PV}{\gamma +1}$
3. $\frac{2PV}{\gamma +1}$
4. $\frac{2PV}{\gamma -1}$

Q.

If there are two objects in thermal equilibrium in one frame, they will be in thermal equilibrium in all frames

1. True

2. False

Q.

The temperature at which the root mean square velocity of a molecule will be doubled than at ${100}^{\circ }C$

1. ${1219}^{\circ }C$

2. ${1492}^{\circ }C$

3. ${400}^{\circ }C$

4. 400 K

Q.

For the theory of equipartition of energy the energy associated with the each molecule is f/ 2 KT if the gas has n number of moles , now how we can convert the moles into molecules and the energy associated with total molecule is found to be n×na×f/2KT. Here na×K=R(gas constant) how? And total energy associated with total molecule is n ×R×T×f/2.

Q.

Name the motion of the molecules of a gas.