= Isothermal compression
An <isothermal compression> reduces the <volume (thermodynamics)> of a <thermodynamic system> at fixed <temperature>. For a fixed-composition <ideal gas> compressed reversibly from $V_i$ to $V_f<V_i$, <isothermal ideal-gas work> gives
$$
W_{\rm by,rev}=nRT\ln(V_f/V_i)<0,\qquad
Q=W_{\rm by,rev}<0,\qquad \Delta U=0.
$$
The surroundings supply positive <work> $W_{\rm on}$, and the <gas> rejects the same amount of <heat> to the <heat bath>. Compressing $1\,\mathrm{mol}$ at $300\,\mathrm K$ from $20$ to $10\,\mathrm L$ requires approximately $1.729\,\mathrm{kJ}$ of <work> input and rejects $1.729\,\mathrm{kJ}$ of <heat>. If that <heat transfer> cannot keep up, the <temperature> rises: the process departs from <isothermal compression> toward <adiabatic compression>. The <finite-rate isothermal piston model> explains the required small <temperature> excess.
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