InterviewSolution
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InterviewSolution
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The volume of a monatomic ideal gas increases linearly with pressure, as shown in Fig. Calculate (a) increase in internal energy, (b) work done by the gas and (c ) heat supplied to the gas. |
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Answer» We know that for a perfect gas, internal energy is given by `U = (pV)/(gamma - 1)` `implies Delta U = (p_(2)V_(2) - p_(1)V_(1))/(gamma - 1)` `:. Delta U = (8 xx 10^(5) xx 0.5 - 4 xx 10^(5) xx 0.2)/(5//3 - 1) = 4.8 xx 10^(5) J` Now, `Delta W = int_(0.2)^(0.5) PdV` Here, p varies with V along a straight line. Therefore, one way say2 `p = kV + V_(0)` At `p = 4 xx 10^(5), V = 0.2 m^(2)` and `p = 8 xx 10^(5), V = 0.5 m^(3)` `4 xx 10^(5) = k xx 0.2 + V_(0)` and `8 xx 10^(5) = k xx 0.5 + V_(0)` Here, `k = (4)/(3) xx 10^(6)` and `V_(0) = (4)/(3) xx 10^(5)` `p = (4)/(3) xx 10^(5) (10 V + 1)` `Delta W = int_(0.2)^(0.5) (4)/(3) xx 10^(5) ((V^(2))/(2))_(0.2)^(0.5) + (4)/(3) xx 10^(5) (V)_(0.2)^(0.5)` `(4)/(3) xx 10^(6) xx (0.21)/(2) + (4)/(3) xx 10^(5) xx 0.3 = 1.8 xx 10^(5) J` By the first law of thermodynamics `Delta Q = Delta U + Delta W` `:. Delta Q = 4.8 10^(5) + 1.8 xx 10^(5) = 6.6 xx 10^(5) J` |
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