How much heat is required to warm \(2.0\,\mathrm{kg}\) of material with \(c=500\,\mathrm{J\,kg^{-1}\,K^{-1}}\) by \(10\,\mathrm{K}\)?

A \(0.40\,\mathrm{kg}\) object absorbs \(1200\,\mathrm{J}\) and its temperature rises by \(6.0\,\mathrm{K}\). Find its specific heat capacity.

An object loses \(850\,\mathrm{J}\) of heat. What is the sign of \(Q\) if the object is the system?

Find the temperature rise of \(0.25\,\mathrm{kg}\) of aluminum with \(c=900\,\mathrm{J\,kg^{-1}\,K^{-1}}\) when it absorbs \(4.5\times10^3\,\mathrm{J}\).

A \(3.0\,\mathrm{kg}\) block has heat capacity \(2400\,\mathrm{J\,K^{-1}}\). Find its specific heat capacity.

A heater supplies \(150\,\mathrm{W}\) to \(0.60\,\mathrm{kg}\) of water with \(c=4190\,\mathrm{J\,kg^{-1}\,K^{-1}}\). Ignoring losses, find the initial rate of temperature rise.

A copper sample and a water sample have the same mass and absorb the same heat. Copper has a smaller specific heat capacity than water. Which has the larger temperature rise? Explain.

A \(0.50\,\mathrm{kg}\) component with \(c=700\,\mathrm{J\,kg^{-1}\,K^{-1}}\) generates thermal energy internally at \(18\,\mathrm{W}\) while losing heat to the surroundings at \(10\,\mathrm{W}\). Find \(dT/dt\).

A material sample of mass \(0.30\,\mathrm{kg}\) is heated electrically at \(24\,\mathrm{W}\). Its temperature rises from \(22\,{}^\circ\mathrm{C}\) to \(30\,{}^\circ\mathrm{C}\) in \(140\,\mathrm{s}\), with negligible heat loss. Estimate \(c\).

Two objects have heat capacities \(C_1\) and \(C_2\). The same positive heat \(Q\) is added to each separately. Derive the ratio of their temperature changes and interpret it.

A body with temperature-dependent heat capacity \(C(T)=C_0(1+\gamma T)\) is heated from \(T_1\) to \(T_2\). Derive the heat input \(Q\).

A device of heat capacity \(C\) receives constant power \(P\) and loses heat at rate \(b(T-T_s)\), where \(T_s\) is surroundings temperature. Derive \(T(t)\) for initial temperature \(T(0)=T_s\), and identify the limiting temperature.