A balloon contains mol of an ideal gas at atm and K when its volume is L

PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A balloon contains n=1.0 n = 1.0\,mol of an ideal gas at P=1.0 P = 1.0\,atm and T=300 T = 300\,K when its volume is V=24.6 V = 24.6\,L. Gas is being added at a rate of dn/dt=0.020 dn/dt = 0.020\,mol·s−1^{-1}, and the balloon is expanding so that dV/dt=0.25 dV/dt = 0.25\,L·s−1^{-1}. If the pressure is maintained at 1.0 atm, which of the following is the closest approximation to the required instantaneous rate of change of temperature dT/dtdT/dt at that moment? (Use R=0.0821 R = 0.0821\,L·atm·mol−1^{-1}·K−1^{-1}.) (a) 9.0 K s−19.0\,\text{K\,s}^{-1} (b) −6.0 K s−1-6.0\,\text{K\,s}^{-1} (c) −3.0 K s−1-3.0\,\text{K\,s}^{-1} (d) −3.0 K s−1\phantom{-}3.0\,\text{K\,s}^{-1}

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