When a sample of an ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P–V curve, V–T curve, P–T curve etc.
For example, P–V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V–T curve for a fixed amount of an ideal gas at constant pressure is a straight line and P–T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.
Now, answer the following questions :
(i) Which of the following statements is correct regarding a fixed amount of ideal gas undergoing the following process :
Text Solution
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(i)b
Temperature decreases during process A to B, so RMS speed decreases (V RMS )
d gas = 
. Upon moving from A to B, P increases and temperature decreases. So, density of gas increases.
This graph is possible if during the process : P ∝ 
.
PT = Constant ∴ P 
= Constant ∴ P 2 V = Constant or PV 1/2 = Constant
If P B = 4P A , then V A = 16V B (according to P 2 V = Constant for process)
(ii)b Equation of straight line
(y – y 1 ) = 
(x – x 1 )
(P – 16) = 
(V – 6)
3P + 4V = 72
T max = 
For (PV) max , 3P = 
and 4V = 
P = 12, V = 9
T max = 
= 648K.
(iii)d This graph is possible if temperature of gas is kept constant and pressure is increased from A to B.
This graph is possible if temperature of gas is increased continuously during the process A to B.
This graph is possible if during the process : P ∝ 
VT = constant ∴ 
= Constant or PV 2 = constant.
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