The balloon contains 0.30 mol of helium starts at a pressure of 125 kPa and rises to an altitude where the pressure is 70.0 kPa , maintaining a constant 300 K temperature. How much work does the gas in the balloon do? W= ____ J
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The equation for work for the situation for constant temperature and non-constant pressure is W=nRT*ln(Vb/Va)
For the problem, we are given n, we know R since it is a constant, we are given T and we can find Vb and Va from the given pressures.
To calculate Va, we can use the ideal gas law, PV=nRT. Therefore, Va = nRT/P = (0.30 mol)(0.0821 L*atm*K^-1*mol^-1)(300 K)/(125 kPa * 0.009869 atm/kPa) = 5.990 L
Similarly, Vb = nRT/P = (0.30 mol)(0.0821 L*atm*K^-1*mol^-1)(300 K)/(70 kPa * 0.009869 atm/kPa) = 10.696 L
Plugging Va and Vb into the equation, we have W=(0.3 mol)(8.314 J*K^-1*mol^-1)(300 K)*ln(10.696 L/5.990 L) = 433.83 J or, when using proper sig figs, 434 J
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