Thermodynamic Question

Problem 1:

A man (the system) walks inside an isolated room for 5 hours and does $W = 1250 J$ of work. The internal energy decreases by $U = 2250 J$ . Determine the heat $Q$ (with sign).

Follow-up:

If the system instead gains

$3000 J$ $3000 J$ of heat while performing the same work ( $W = 1250 J$ ), what is the change in internal energy?

Problem 2:
At constant pressure $p = 2.5 10^{5} Pa$ , the system does $W = 4500 J$ of work. Find the change in volume $V$ .

Problem 3:
An isothermal compression of an ideal gas: $n = 4$ moles, initial temperature $T = 375 K$ . The gas is compressed to one-fifth of its initial volume ( $V_{f} = V_{i} / 5$ ). How much heat is removed during the compression?

Problem 4:
A car engine with efficiency $= 30.0 %$ produces $W = 4000 J$ of work. How much heat is rejected by the engine?

Problem 5:
A Carnot (ideal) heat pump heats a house kept at $T_{H} = 300 K$ ; outside temperature is $T_{C} = 265 K$ . How much work must the pump do to deliver $Q_{H} = 5000 J$ of heat into the house?

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