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Question

# In the P-V diagram shown in figure, choose the correct options for the process a - b

A
density of gas reduced to half
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B
temperature of gas has increased to two times
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C
internal energy of gas has increased to four times
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D
T - V graphs is a pararabola passing through origin.
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Solution

## The correct options are A density of gas reduced to half C internal energy of gas has increased to four times D T - V graphs is a pararabola passing through origin.Clearly the volume has become doubled.Thus the density=mV becomes half of initial value.For an ideal gas, PV=nRT⟹T∝PVSince both P,V double, the T becomes four times. Internal energy is proportional to temperature of the gas. Thus it also becomes four times.Since P-V curve has a constant slope, PV=k⟹P=kVUsing the relation in ideal gas equation gives,(kV)V=nRT⟹kV2=nRTThus T-V graph is a parabola passing through origin.

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