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I've been trying to tackle the following problem, but I can't seem to get it right.
An ideal monatomic gas expands quasi-statically to twice its volume. If the process is isothermal, the work done by the gas is W_i. If the process is adiabatic, the work doen by the gas is W_a. Show that 0 < W_a < W_i.
For isothermal processes I have
[tex]
W_i = \int_{v_i}^{v_f} \frac{nRT}{V}dV = nRT ln(2)
[/tex]
For adiabatic processes I have
[tex]
W_a = k \int_{v_i}^{v_f} \frac{dV}{V^{\gamma}}
[/tex]
Where do go from this point?
An ideal monatomic gas expands quasi-statically to twice its volume. If the process is isothermal, the work done by the gas is W_i. If the process is adiabatic, the work doen by the gas is W_a. Show that 0 < W_a < W_i.
For isothermal processes I have
[tex]
W_i = \int_{v_i}^{v_f} \frac{nRT}{V}dV = nRT ln(2)
[/tex]
For adiabatic processes I have
[tex]
W_a = k \int_{v_i}^{v_f} \frac{dV}{V^{\gamma}}
[/tex]
Where do go from this point?