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Question
Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P1 and P2?
Options
P1 > P2
P1 = P2
P1 < P2
data is insufficient.
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Solution
P1 > P2
Explanation:
As we know that the pressure and the quantity of gas in the system are constants. Thus, by using the ideal gas equation
PV = nRT
V ∝ T .....(When n, P and R are constants)
`V_1/T_1` = constant
Or slope of graph is constant
`V = (nRT)/P`
`(dV)/(dT) = (nR)/P`
Or `(dV)/(dT)` increases when P decreases
Thus, `(dV)/(dT) ∝ 1/P`
This shows that slope P1 is smaller than P2.
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