1st Law of Thermodynamics

Q. A body cools from a temperature $3T$ to $2T$ in $10$ minutes. The room temperature is $T$. Assume that Newton's law of cooling is applicable, the temperature of the body at the end of next $10$ minutes will be

1. $\frac{4}{3}T$
2. $T$
3. $\frac{7}{4}T$
4. $\frac{3}{2}T$

Q. A sample of $0.1\text{g}$ of water at ${100}^{\circ }\text{C}$ and normal pressure $(1.03\times {10}^5{\text{Nm}}^{-2})$ requires $54\text{cal}$ of heat energy to convert to steam at ${100}^{\circ }\text{C}$. If the volume of the steam produced is $167.1\text{cc}$, the change in internal energy of the sample is

1. $+104.4\text{J}$
2. $+208.8\text{J}$
3. $-84.5\text{J}$
4. $-242.6\text{J}$

Q. In a thermodynamic process, pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20\text{J}$ of heat, when $8\text{J}$ of work is done on the gas. If the initial internal energy of the gas was $30\text{J}$, then the final internal energy will be

1. $+42\text{J}$
2. $+18\text{J}$
3. $-18\text{J}$
4. $-42\text{J}$

Q.

What is the difference between heat and temperature?

Q.

A Carnots engine working between $400K$ and $800K$has a work output of $1200J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :

1. $1800J$

2. $3200J$

3. $2400J$

4. $1600J$

Q.

Convert a speed of $54$ km per hour into meter per second.

Q.

How is the first law of thermodynamics derived?

Q.

A gas mixture consists $3moles$ of oxygen and $5moles$ argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of $RT$) of the mixture is:

1. $11$

2. $13$

3. $15$

4. $20$

Q. A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i={10}^{5}Pa$ and volume $V_i={10}^{-3}Pa$ changes to a final state at $P_f=\left(\frac{1}{32}\right)\times {10}^{5}Pa$ and $V_f=8\times {10}^{-3}{m}^3$ in an adiabatic quasi-static process, such that $P^3{V}^5=$ constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps : an isobaric expansion at $P_i$ followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately

1. $112J$
2. $294J$
3. $588J$
4. $813J$

Q.

Give that the time period T of ossilation of a gas bubble from an explosion under water depends uopon P, D and E ehere P is the static pressure, D is the density of water and E is the total energy of explosion, find dimensionally the relation of T.

Q.

A gas is taken through a cyclic process ABCA as shown in figure. If 2.4 cal of heat is given in the process, what is the value of J ?

Q. In a thermodynamic process, pressure of a fixed mass of gas is changed in such a manner that the gas releases $20\text{J}$ of heat and $8\text{J}$ of work is done on the gas. If initial internal energy of the gas was $30\text{J}$, then the final internal energy will be

1. $42\text{J}$
2. $18\text{J}$
3. $12\text{J}$
4. $60\text{J}$

Q. An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity $C$ remains constant. If during this process, the relation of pressure $P$ and volume $V$ is given by $P{V}^n=constant$, then $n$ is given by (Here $C_P$ and $C_V$ are molar specific heat at constant pressure and constant volume, respectively)

1. $\begin{array}{c}n=\frac{C_p}{C_v}\end{array}$
2. $\begin{array}{c}n=\frac{C-C_p}{C-C_v}\end{array}$
3. $\begin{array}{c}n=\frac{C_p-C}{C-C_v}\end{array}$
4. $\begin{array}{c}\\ n=\frac{C-C_v}{C-C_p}\end{array}$

Q. The change in internal energy of a system that has absorbed $2\text{kcal}$ of heat and does $500\text{J}$ of work is

1. $6400\text{J}$
2. $5400\text{J}$
3. $7860\text{J}$
4. $8900\text{J}$

Q. An isolated system is a system in which

1. there is no exchange of energy with the surrounding.
2. there is exchange of mass and energy with the surrounding.
3. there is no exchange of energy and mass with the surrounding.
4. there is no exchange of mass with the surrounding.

Q. In a certain process, $400\text{cal}$ of heat is supplied to a system and at the same time $105\text{J}$ of mechanical work was done on the system. The increase in its internal energy is

1. $425\text{cal}$
2. $375\text{cal}$
3. $505\text{cal}$
4. $295\text{cal}$

Q.

One mole of ideal monoatomic gas $(\gamma =\frac{5}{3})$ is mixed with one mole of diatomic gas $(\gamma =\frac{7}{5})$. What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure, to that at constant volume.

1. $\frac{3}{2}$

2. $\frac{35}{23}$

3. $\frac{4}{3}$

4. $\frac{23}{15}$

Q.

$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that

$C_p-C_v=a$ for hydrogen gas

$C_p-C_v=b$ for nitrogen gas

The correct relation between $a$ and $b$ is

1. $a=\frac{1}{14b}$

2. $a=b$

3. $a=14b$

4. $a=28b$

Q. If two moles of diatomic gas and one mole of monoatomic gas are mixed, then the ratio of specific heats is

1. 
2. 
3. 
4. 

Q. The latent heat of vaporization of water is $2240\text{J/g}$. If the work done in the process of expansion of $1\text{g}$ is $168\text{J}$, then increase in internal energy is

1. $2408\text{J}$
2. $2240\text{J}$
3. $2072\text{J}$
4. $1904\text{J}$

Q.

What are the types of boundaries in Thermodynamics?

Q. Volume of 1 equivalent O2 gas at STP is 22.4L 11.2L 5.6L 9.8L

Q.

A Carnot engine working between 300K and 600K has work output of 800 J per cycle. What is amount of heat energy supplied to the engine from source per cycle

1. 1800 J/cycle

2. 1000 J/cycle

3. 2000 J/cycle

4. 1600 J/cycle

Q. A gas is compressed at a constant pressure of $50{\text{N/m}}^2$ from a volume of $10{\text{m}}^3$ to a volume of $4{\text{m}}^3$. Heat of $100\text{J}$ is then added to the gas by heating. Its internal energy is

1. Decreased by $200\text{J}$
2. Decreased by $400\text{J}$
3. Increased by $400\text{J}$
4. Increased by $200\text{J}$

Q.

Figure 17.5 shows the P - V diagram for a fixed mass of an ideal gas undergoing cyclic process ABCA.AB represents isothermal process. Which of the graphs shown in Fig. 17.6 represents the P - T diagram of the cyclic process ?

1. 
   

2. 
   

3. 
   

4. 
   

Q.

Figure shows a paddle wheel coupled to a mass of 12 kg through fixed frictionless pulleys. The paddle is immersed in a liquid of heat capacity $4200\text{J}{K}^{-1}$ kept in an adiabatic container. Consider a time interval in which the 12 kg block falls slowly through 70 cm.

(a) How much heat is given to the liquid ?

(b) How much work is done on the liquid ?

(c) Calculate the rise in the temperature of the liquid neglecting the heat capacity of the container and the paddle.

Q. A perfect gas goes from a state $A$ to state $B$ by absorbing $8\times {10}^5\text{J}$ and by doing $6.5\times {10}^5\text{J}$ of external work. It is taken from same initial state $A$ to final state $B$ in another process in which it absorbs ${10}^5\text{J}$ of heat, then work done in the second process

1. on gas is ${10}^5\text{J}$
2. on gas is $0.5\times {10}^5\text{J}$
3. by gas is ${10}^5\text{J}$
4. by gas is $0.5\times {10}^5\text{J}$

Q.

What is the relation between H and U?

Q. 5 moles of Hydrogen $(\gamma =\frac{7}{5})$ initially at S.T.P. are compressed adiabatically so that its temperature becomes ${400}^{o}C$. The increase in the internal energy of the gas in kilo - joules is: $(R=8.30Jmo{l}^{-1}{K}^{-1})$

1. 65.55
2. 80.55
3. 21.55
4. 41.5

Q. Four identical samples of an ideal gas are taken along the paths $A,B,C$ and $D$ from state $1$ to state $2$ as shown in the $PV$ indicator diagram. Let $Q,W$ and $\Delta U$ represent the heat supplied, work done and change in internal energy of the gas respectively. Choose the correct option among the following :

1. $Q_A-Q_D=W_A-W_D$
2. $W_A<W_B<W_C<W_D$
3. $Q_B-W_B>Q_C-W_C$
4. $Q_A<Q_B<Q_C<Q_D$