Single Choice

A cyclic process for $$1\ mole$$ of an ideal gas is shown in the $$V-T$$ diagram. The work done in $$AB, BC$$ and $$CA$$ respectively is

A$$0,\, TR_2\, \ln\, \left | \displaystyle \dfrac{V_2}{V_1} \right |,\, R(T_1\, -\, T_2)$$
B$$R(T_1\, -\, T_2),\, 0,\, RT_1\, \ln\, \left |\displaystyle \dfrac{V_1}{V_2} \right |$$
C$$0,\, RT_1\, \ln\, \left |\displaystyle \dfrac{V_2}{V_1} \right |, \dfrac{RT_1}{V_1}(T_1\, -\, T_2)$$
D$$0,\, RT_2\, \ln\, \left | \displaystyle \dfrac{V_2}{V_1} \right |,\, R(T_1\, -\, T_2)$$
Correct Answer

Solution

$$PV=nRT\\ P\propto T\\ V\propto T$$
Work Done , $$W=\int { PdV } $$

For Process A-B
Volume is constant and temperature is increasing.
Therefore, Work Done is Zero.

For Process B-C:
Volume is increasing with temperature being constant. So insentropic process.
Therefore, Work Done = $$R{ T }_{ 2 }\ \ln\dfrac { { V }_{ 2 } }{ { V }_{ 1 } } $$

For Process C-A:
Volume is decreasing linearly with temperature. Therefore, P=cT kind of equation.
Therefore, Work Done = $$\int _{ V2 }^{ V1 }{ P } dV\quad =\quad R({ T }_{ 1 }-{ T }_{ 2 })$$

SIMILAR QUESTIONS

Thermodynamics

Two points $$\mathrm{P}$$ and $$\mathrm{Q}$$ are maintained at the potentials of $$10\ \mathrm{V}$$ and $$-4\mathrm{V}$$, respectively. The work done in moving 100 electrons from $$\mathrm{P}$$ to $$\mathrm{Q}$$ is :

Thermodynamics

A sample of $$0.1\ g$$ of water at $$100^{o}\ C$$ and normal pressure $$(1.013\times 10^{5}\ Nm^{-2})$$ requires $$54$$ cal of heat energy of convert to steam at $$100^{o}\ C$$. If the volume of the steam produced is $$167.1\ cc$$, the change in internal energy of the sample, is?

Thermodynamics

For cyclic process which of the following quantity is zero?

Thermodynamics

In a cyclic process, work done by the system is

Thermodynamics

1 Liter of an ideal gas $$ (\gamma-1.5) $$ at 300 k=K is suddenly compressed to half its original volume. (a) Find the ratio of the final pressure to the initial pressure (b) If the original pressure is 100 kPa, find the work done by gas in the process. (c) What is the change in internal energy? (d) What is the final temperature? (e) The gas is now cooled to 300K keeping its pressure constant: Calculate the work done during the process. (f)The gas is now expanded isothermally to achieve its original volume of 1 litre. Calculate the work done by the gas. (g) Calculate the total work done in the cycle.

Thermodynamics

When a system is taken through the process abc shown in figure , $$80 J$$ of heat is absorbed by the system and $$30 J$$ of work is done by it. If the system does $$10 J$$. of work during process $$adc$$, how much heat flows into it during the process?

Thermodynamics

As a result of the isobaric heating by $$\Delta T = 72 \ K$$ one mole of a certain ideal gas obtains an amount of heat $$Q = 1.60 \ kJ$$. Find the work performed by the gas, the increment of its, internal energy, and the value of $$\gamma = C_p/C_v$$.

Thermodynamics

LA certain mass of nitrogen was compressed $$\eta = 5.0$$ times (in terms of volume), first adiabatically, and then isothermally. In both cases the initial state of the gas was the same. Find the ratio of the respective works expended in each compression.

Thermodynamics

Demonstrate that the process in which the work performed by an ideal gas is proportional to the corresponding increment of its internal energy is described by the equation $$pV^n$$ = coast, where $$n$$ is a constant.

Thermodynamics

One mole of argon is expanded polytropically, the polytropic constant being $$n = 1.50$$. In the process, the gas temperature changes by $$\Delta T = - 26 \ K$$. Find: (a) the amount of heat obtained by the gas; (b) the work performed by the gas.

Contact Details