Heat Engines

Q. An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are $Q_1=5960\text{J}$, $Q_2=-5585\text{J}$, $Q_3=-2980\text{J}$ and $Q_4=3645\text{J}$ respectively. The corresponding quantities of work involved are $W_1=2200\text{J}$, $W_2=-825\text{J},W_3=-1100\text{J}$ and $W_4$ respectively . Find the efficiency of the cycle.

1. $10.82\%$
2. $30.86\%$
3. $17.44\%$
4. $28.53\%$

Q.

What is the first three laws of thermodynamics?

Q.

What are the first and second laws of thermodynamics?

Q. A carnot engine, whose efficiency is 40% takes in heat from a source maintained at a temperature of $500\text{K}$. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) must be

1. efficiency of carnot engine cannot be made larger than 50%
2. $1200\text{K}$
3. $750\text{K}$
4. $600\text{K}$

Q. Helium gas goes through a cycle $\text{ABCDA}$ (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly:
[Assume the gas to be an ideal gas]

1. $15.4\%$
2. $10.5\%$
3. $9.1\%$
4. $12.5\%$

Q. Two Carnot engines $A$ and $B$ are operated in series. The first engine $A$, receives heat at $800\text{K}$and rejects to a reservoir at temperature $T$. The second engine $B$ receives the heat rejected by the first engine and in turn rejects to a heat reservoir at $300\text{K}$. Find the value of $T$, when the work outputs of the engines are equal.

1. $0\text{K}$
2. $1100\text{K}$
3. $550\text{K}$
4. $300\text{K}$

Q. An ideal monoatomic gas undergoes the cyclic process $\text{ABCDA}$ as shown in the figure. The efficiency of the cycle is

1. $28.6\%$
2. $19.04\%$
3. $46.8\%$
4. $62.3\%$

Q. A Carnot heat engine works between the temperatures ${427}^{\circ }\text{C}$ and ${27}^{\circ }\text{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0\text{kW}$?

1. $418\text{cal/s}$
2. $41.8\text{cal/s}$
3. $4.18\text{cal/s}$
4. $0.418\text{cal/s}$

Q. In a Carnot heat engine, the temperature of source and sink are $500\text{K}$ and $375\text{K}$. If the engine consumes $25\times {10}^5\text{J}$ per cycle, then work done by engine per cycle is

1. $6.25\times {10}^5\text{J}$
2. $100\times {10}^5\text{J}$
3. $2.5\times {10}^5\text{J}$
4. $0.625\times {10}^5\text{J}$

Q. The $P-V$ diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process $CD$ is $(\text{use}\gamma =1.4):$

1. $–400\text{J}$
2. $–500\text{J}$
3. $200\text{J}$
4. $400\text{J}$

Q.

A pump motor is used to deliver water at a certain rate from a given pipe to a certain height. To obtain twice as much water from the same pipe in the same time, power of the motor has to be increased to

1. 16 times

2. 4 times

3. 8 times

4. 2 times

Q. The number of molecules in one litre of an ideal gas at $300\text{K}$ and $2$ atmospheric pressure with mean kinetic energy $2\times {10}^{–9}\text{J}$ per molecule is :

1. $3\times {10}^{11}$
2. $1.5\times {10}^{11}$
3. $0.75\times {10}^{11}$
4. $6\times {10}^{11}$

Q. A cyclic process ABCA is shown in the V-T diagram. Process on the P-V diagram is

1. 
2. 
3. 
4. 

Q. In a Carnot heat engine, the temperature of source and sink are ${827}^{\circ }\text{C}$ and ${27}^{\circ }\text{C}$. If the engine consumes $33\text{kJ}$ per cycle, then the heat rejected to the sink per cycle is

1. $9\text{kJ}$
2. $24\text{kJ}$
3. $11\text{kJ}$
4. $10\text{kJ}$

Q. An ideal reversible heat engine converts one sixth of the heat input into work. If the temperature of the sink is reduced by ${62}^{\circ }C$, its efficiency is doubled. Find the temperature of the source and sink respectively (In $\text{Kelvin}$).

1. $372,310$
2. $372,248$
3. $472,310$
4. $325,375$

Q.

What is the full form of ITUS?

Q. An engine operates by taking a monoatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ______.

Q. Number of molecules in a volume of $4{\text{cm}}^3$ of a perfect monoatomic gas at some temperature $T$ and at a pressure of $2\text{cm}$ of mercury is close to ?
(Given, mean kinetic energy of a molecule (at $T$) is $4\times {10}^{-14}\text{erg},g=980{\text{cm/s}}^2$, density of mercury $=13.6{\text{g/cm}}^3$)

1. $4.0\times {10}^{18}$
2. $4.0\times {10}^{16}$
3. $5.8\times {10}^{16}$
4. $5.8\times {10}^{18}$

Q. The area enclosed by a $PV$ graph for one thermodynamic cycle of a heat engine is $610\text{J}$. The total thermal energy absorbed by the gas in one cycle is $1300\text{J}$. Determine the efficiency of the cycle.

1. $47\%$
2. $23\%$
3. $36.8\%$
4. $9.4\%$

Q. One mole of a monoatomic gas of molar mass $M$ undergoes a cyclic process as shown in the figure. Here, $\rho$ is the density and $P$ is the pressure of the gas. Find the efficiency of the cycle.

1. $\frac{3}{5}(1-\ln 2)$
2. $\frac{3}{5}\ln 2$
3. $\frac{2\ln 2}{5}$
4. $\frac{2}{5}(1-\ln 2)$

Q. One mole of a diatomic ideal gas $(\gamma =1.4)$ is taken through a cyclic process starting from point $A$. The process $A\to B$ is an adiabatic compression, $B\to C$ is an isobaric expansion, $C\to D$ is an adibatic expansion and $D\to A$ is an isochoric process. The volume ratios are $\frac{V_A}{V_B}=16,\frac{V_C}{V_B}=2$ and temperature $T_A={27}^{\circ }\text{C}$. Find the efficiency of the cycle.

1. $32.84\%$
2. $61.40\%$
3. $28.56\%$
4. $35.61\%$

Q. An ideal gas is taken through the cycle ABCA a shown in the P-V diagram. The total work done by the gas during the cycle is

1. pV
2. 3pV
3. 6pV
4. 2pV

Q. Calculate the thermal efficiency of a Carnot's heat engine working between ice point and steam point.

1. $26.81\%$
2. $12.97\%$
3. $33.33\%$
4. $83.19\%$

Q. A gas undergoes a cyclic process $a\to b\to c\to a$ which is as shown in the $PV$ diagram. The process $a\to b$ is isothermal , $b\to c$ is adiabatic and $c\to a$ is a straight line on the $P-V$ diagram. Work done in process $ab$ and $bc$ is $5\text{J}$ and $4\text{J}$ respectively. Calculate the efficiency of the cycle, if the area enclosed by the diagram $\text{abca}$ in the figure is $3\text{J}$.

1. $0.6$
2. $0.75$
3. $0.8$
4. $0.4$

Q. Find the efficiency of the thermodynamic cycle shown in figure for an ideal diatomic gas.

1. $\frac{1}{4}$
2. $\frac{1}{9}$
3. $\frac{1}{8}$
4. $\frac{1}{18}$

Q.

Determine the time taken by a 500 W heater to raise the temperature of 50 kg of material of specific heat capacity $920\mathrm{J}.{\mathrm{kg}}^{-1}.{\mathrm{K}}^{-1}$, from ${18}^{\circ }\mathrm{C}$ to ${38}^{\circ }\mathrm{C}$. Assume that all the heat supplied by the heater is given to the material.

Q. Two vessels of the same volume contain the same ideal gas at the same temperature. If the pressure in the vessels are in the ratio of 1 : 2, then

1. The ratio of the average kinetic energies is 1 : 2
2. The ratio of the root mean square velocities is 1 : 1
3. The ratio of the average velocities is 1 : 2
4. The ratio of the number of molecules is 1 : 2

Q. An ideal gas changes state as shown in the figure. What is the work done by the gas in the process?

1. Infinite
2. Zero
3. Negative
4. Positive

Q. The heat rejected per cycle by a heat engine to the surroundings is $60\%$ of the heat supplied. Find the efficiency of heat engine.

1. $60\%$
2. $40\%$
3. $20\%$
4. $75\%$

Q.

Are heat engines reversible?