an ideal gas is subjected to cyclic process involving four

An ideal gas is subjected to cyclic process involving four thermodynamic states, the amounts of heat $$\left( Q \right)$$ and work $$\left( W \right)$$ involved in each of these states
$${Q_1} = 6000\,J;{Q_2} = - 5500\,J;{Q_3} = - 3000\,J;{Q_4} = + 3500\,J$$
$${W_1} = 2500\,J;{W_2} = - 1000\,J;{W_3} = - 1200\,J;{W_4} = xJ$$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $$\eta .$$ The values of $$x$$ and $$\eta $$ respectively are

A. 500; 7.5%

B. 700; 10.5%

C. 1000; 21%

D. 1500; 15%

Answer : 700; 10.5%

Solution :
$$\eqalign{ & Q = {Q_1} + {Q_2} + {Q_3} + {Q_4} \cr & = 6000 - 5500 - 3000 + 3500 = + 1000\,J \cr & W = {W_1} + {W_2} + {W_3} + {W_4} \cr & = 2500 - 1000 - 1200 + x = + 300 + x \cr} $$
In cyclic process, $$\Delta U = 0$$
Now, $$Q = \Delta U + W$$
$$\eqalign{ & {\text{or}}\,\,1000 = 0 + \left( {300 + x} \right) \cr & \therefore x = 700\,J \cr & \eta = \frac{W}{{{Q_1} + {Q_4}}} \cr & = \frac{{1000}}{{6000 + 3500}} = 10.5\% \cr} $$

Releted MCQ Question on
Heat and Thermodynamics >> Thermodynamics

Releted Question 1

An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is

A. $$PV$$

B. $$2PV$$

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

D. zero

View Answer

Releted Question 2

If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is

A. 1.40

B. 1.50

C. 1.53

D. 3.07

View Answer

Releted Question 3

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A. same everywhere

B. lower in the front side

C. lower in the rear side

D. lower in the upper side

View Answer

Releted Question 4

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is

A. $$4\, RT$$

B. $$15\, RT$$

C. $$9\, RT$$

D. $$11\, RT$$

View Answer

Releted MCQ Question on
Heat and Thermodynamics >> Thermodynamics

An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is

If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is

Practice More Releted MCQ Question on
Thermodynamics

Practice More MCQ Question on Physics Section

Releted MCQ Question on Heat and Thermodynamics >> Thermodynamics

An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is

If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is

A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is

A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is

Practice More Releted MCQ Question on Thermodynamics

Practice More MCQ Question on Physics Section

Releted MCQ Question on
Heat and Thermodynamics >> Thermodynamics

Practice More Releted MCQ Question on
Thermodynamics