First slide

Heat given

Question

One mole of an ideal monoatomic gas is heated from state point A to state point C according to the process A-B-C as shown in figure. Then total heat supplied to the gas is

Easy

A

$3 P_{0} V_{0}$
B

$\frac{5}{2} P_{0} V_{0}$
C

$\frac{3}{2} P_{0} V_{0}$
D

$4 P_{0} V_{0}$

Solution

Process AB is a straight line and passes through the origin. So AB is isochoric process i.e. $V_{B} = V_{0}$
$∴ \frac{2 P_{0} . V_{0}}{T_{B}} = \frac{P_{0} V_{0}}{T_{0}} \Rightarrow T_{B} = 2 T_{0}$
$∴ Q = Q_{A B} + Q_{B C} = n . C_{V} . (T_{B} - T_{A}) + n . C_{P} . (T_{C} - T_{B})$
$\Rightarrow Q = 1 \frac{3 R}{2} (2 T_{0} - T_{0}) + 1 \frac{5 R}{2} (3 T_{0} - 2 T_{0}) = 4 R T_{0} = 4 P_{0} V_{0}$

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