An ideal gas (γ = 1.67) is taken through the process abc shown in figure. The temperature at the point a is 300K. Calculate

(a) the temperature at b and c,

(b) the work done in the process,

(c) the amount of heat supplied in the path ab and in the path bc and

(d) the change in the internal energy of the gas in the process.

Let (P1, V1, T1), (P2, V2, T2), (P3, V3, T3) denote the pressure, volume and temperature at a, b and c respectively.

(a)For the process ab volume is constant

I.e. by ideal gas equation,

, temperature at b

For the process bc, pressure is constant.

By ideal gas equation,

temperature at c

(b)Here process ab is isochoric i.e. W_{ab}=0

For process bc, P=200 kPa, change in volume is 50 cm^{3} from b to c

(c) From the first law of thermodynamics,

Where dQ is the amount of heat supplied

As ab is isochoric process dW=0

Here bc is an isobaric process where heat supplied dQ by first law of

Thermodynamics is

(d) dQ = dU + W

Now

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