An object has mass \(0.60\,\mathrm{kg}\) and specific heat capacity \(800\,\mathrm{J\,kg^{-1}\,K^{-1}}\). Find its heat capacity.

How much heat is required to raise \(3.0\,\mathrm{mol}\) of a substance by \(12\,\mathrm{K}\) if its molar heat capacity is \(25\,\mathrm{J\,mol^{-1}\,K^{-1}}\)?

A sample has total heat capacity \(150\,\mathrm{J\,K^{-1}}\) and amount \(2.0\,\mathrm{mol}\). Find its molar heat capacity.

A \(0.25\,\mathrm{kg}\) sample absorbs \(1800\,\mathrm{J}\) and warms by \(8.0\,\mathrm{K}\). Find its specific heat capacity.

A monatomic ideal gas has three active translational quadratic degrees of freedom. Use equipartition to estimate \(C_{V,m}\).

A classical crystalline solid has six active quadratic energy terms per atom. Estimate its molar heat capacity in terms of \(R\), then numerically with \(R=8.31\,\mathrm{J\,mol^{-1}\,K^{-1}}\).

A substance has \(c=500\,\mathrm{J\,kg^{-1}\,K^{-1}}\) and molar mass \(0.040\,\mathrm{kg\,mol^{-1}}\). Find its molar heat capacity.

A gas has measured \(C_{V,m}=20.8\,\mathrm{J\,mol^{-1}\,K^{-1}}\). Estimate the number of active quadratic degrees of freedom \(f\) using \(C_{V,m}=fR/2\).

Explain why heat capacity can depend on temperature even when the amount of substance is fixed.

A material has molar heat capacity \(C_m(T)=A+BT\). Derive the heat required to warm \(n\) moles from \(T_1\) to \(T_2\).

A \(0.30\,\mathrm{kg}\) piece with \(c=900\,\mathrm{J\,kg^{-1}\,K^{-1}}\) is joined to a \(0.50\,\mathrm{kg}\) piece with \(c=450\,\mathrm{J\,kg^{-1}\,K^{-1}}\). How much heat is required to raise the combined object by \(20\,\mathrm{K}\), and what is its effective specific heat capacity?

A \(2.0\,\mathrm{mol}\) ideal gas absorbs \(1.66\,\mathrm{kJ}\) at constant volume while its temperature rises by \(40\,\mathrm{K}\). Estimate the number of active quadratic degrees of freedom \(f\), using \(C_{V,m}=fR/2\).

A sample has \(C_m=25.0\,\mathrm{J\,mol^{-1}\,K^{-1}}\) and amount \(0.600\,\mathrm{mol}\). Find the heat needed for a \(30.0\,\mathrm K\) temperature rise.

A material has specific heat capacity \(c=390\,\mathrm{J\,kg^{-1}\,K^{-1}}\) and molar mass \(6.35\times10^{-2}\,\mathrm{kg\,mol^{-1}}\). Find its molar heat capacity.

A low-temperature solid has measured molar heat capacity much less than \(3R\). Explain why this does not contradict the high-temperature equipartition result.

Derive the relation \(C=mc=nC_m\) for a uniform sample.

Starting from equipartition, derive \(C_{V,m}=fR/2\) for an ideal gas with \(f\) active quadratic degrees of freedom.

A heat capacity measurement changes abruptly near a temperature. Give a molecular or material reason this can happen.

Explain why heat capacity is a property of a chosen process for gases, but specific heat capacity of a solid is often treated as a material property.

For \(C_m(T)=A+BT+DT^2\), derive the heat needed for \(n\) moles from \(T_1\) to \(T_2\).