First slide

First law of thermodynamics

Question

An ideal gas is taken through the cycle $A \to B \to C \to A$ , as shown in figure. If the net heat supplied to the gas in the cycle is 5 J, work done by the gas in the process $C \to A$

Moderate

A

-5 J
B

-10 J
C

-15 J
D

-20 J

Solution

${given graph has pressure along horizontal axis, volume in meter}^{3} along vertical axis$
$w o r k d o n e f r o m A t o B i s W_{A \to B} =PdV=10 [2-1] =10 J, here volume is increased$
$w o r k d o n e f r o m B t o C i s W_{B \to C} =PdV=0, here there is no change in volume$
$w o r k d o n e f r o m C t o A i s W_{C \to A} =?$
In cyclic process $dU=0$ ,( change in internal energy)
$\begin{array}{rcl} from first law of thermodynamics dQ=dU+dW \\ h e r e dQ & = & c h a n g e i n h e a t e n e r g y = 5 J \\ dU & = & c h a n g e i n i n e r n a l e n e r g y \\ dW & = & w o r k d o n e \\ s u b s t i t u t e i n first law of thermodynamics \end{array}$
$\begin{array}{rcl} \Rightarrow & 5=0+ [W_{A \to B} {+W}_{B \to C} {+W}_{C \to A}] \\ \Rightarrow & {5=10+0+W}_{C \to A} \end{array}$
$\begin{array}{rcl} \Rightarrow & W_{C \to A} = 5 - 10 \\ \Rightarrow & W_{C \to A} = - 5 J \end{array}$

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