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

Question

Quantrex Academy · Accepted Answer

Correct answer: A. 600 K , 900 K

From the given graph, the pressure and volume at points

a

,

b

, and

c

are:

P_a = 100 \text{ kPa}

,

V_a = 100 \text{ cm}^3

P_b = 200 \text{ kPa}

,

V_b = 100 \text{ cm}^3

P_c = 200 \text{ kPa}

,

V_c = 150 \text{ cm}^3

Using the ideal gas equation,

\dfrac{PV}{T} = \text{constant}

.

For the isochoric process

a \to b

(

V = \text{constant}

):

\dfrac{P_a}{T_a} = \dfrac{P_b}{T_b}

\Rightarrow T_b = T_a \times \dfrac{P_b}{P_a} = 300 \times \dfrac{200}{100} = 600 \text{ K}

For the isobaric process

b \to c

(

P = \text{constant}

):

\dfrac{V_b}{T_b} = \dfrac{V_c}{T_c}

\Rightarrow T_c = T_b \times \dfrac{V_c}{V_b} = 600 \times \dfrac{150}{100} = 900 \text{ K}

The temperatures at

b

and

c

are

600 \text{ K}

and

900 \text{ K}

respectively.

An ideal gas ( γ = 1.67 ) is taken through the process abc shown in...

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