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The pressure of an ideal gas varies with volume as P=α V, where α is a constant. One mole of the gas is allowed to expand such that its volume becomes m times its initial volume. The work done by the gas in the process is
Asked in JEE Main 2012 · Work from a Stated P-V Law
- (1) (α V)/2(m²-1)
- (2) (α²V²)/2(m²-1)
- (3) α/(2V)(m²-1)
- (4) (α V²)/2(m²-1)
Answer: (4) (α V²)/2(m²-1)
Step-by-step solution
W=∫_V^mVP dV=∫_V^mVα V dV=α/2[(mV)²-V²].
W=(α V²)/2(m²-1).
Why the other options are wrong
- (1) comes from is missing one power of V; check the dimensions of α V dV
- (2) comes from squares α as well as V
- (3) comes from divides by V instead of multiplying
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