How much heat is required to melt \(0.020\,\mathrm{kg}\) of ice at \(0\,{}^\circ\mathrm{C}\)? Use \(L_f=3.34\times10^5\,\mathrm{J\,kg^{-1}}\).

How much heat is released when \(0.010\,\mathrm{kg}\) of steam condenses at its boiling temperature? Use \(L_v=2.26\times10^6\,\mathrm{J\,kg^{-1}}\).

Why does the temperature of a pure melting substance remain constant while heat is still being added?

A \(0.30\,\mathrm{kg}\) water sample at \(20\,{}^\circ\mathrm{C}\) is mixed with \(0.20\,\mathrm{kg}\) water at \(70\,{}^\circ\mathrm{C}\). Find the final temperature, ignoring surroundings.

A \(0.50\,\mathrm{kg}\) metal block with \(c=390\,\mathrm{J\,kg^{-1}\,K^{-1}}\) cools from \(90\,{}^\circ\mathrm{C}\) to \(30\,{}^\circ\mathrm{C}\). Find \(Q\) for the block.

A \(0.040\,\mathrm{kg}\) ice sample at \(0\,{}^\circ\mathrm{C}\) is supplied \(10.0\,\mathrm{kJ}\). What mass melts? Use \(L_f=3.34\times10^5\,\mathrm{J\,kg^{-1}}\).

A \(0.10\,\mathrm{kg}\) water sample at \(100\,{}^\circ\mathrm{C}\) is supplied \(60\,\mathrm{kJ}\). What fraction vaporizes? Use \(L_v=2.26\times10^6\,\mathrm{J\,kg^{-1}}\).

A \(0.050\,\mathrm{kg}\) ice cube at \(0\,{}^\circ\mathrm{C}\) is placed in \(0.40\,\mathrm{kg}\) of water at \(30\,{}^\circ\mathrm{C}\). Use \(c_w=4190\,\mathrm{J\,kg^{-1}\,K^{-1}}\) and \(L_f=3.34\times10^5\,\mathrm{J\,kg^{-1}}\). Does all the ice melt?

A \(0.20\,\mathrm{kg}\) metal sample at \(160\,{}^\circ\mathrm{C}\) is dropped into \(0.30\,\mathrm{kg}\) of water at \(20\,{}^\circ\mathrm{C}\). The final temperature is \(28\,{}^\circ\mathrm{C}\). Estimate the metal's specific heat, ignoring the container.

A \(0.030\,\mathrm{kg}\) ice sample starts at \(-12\,{}^\circ\mathrm{C}\). Find the heat required to warm it to \(0\,{}^\circ\mathrm{C}\) and melt it completely. Use \(c_{\mathrm{ice}}=2100\,\mathrm{J\,kg^{-1}\,K^{-1}}\) and \(L_f=3.34\times10^5\,\mathrm{J\,kg^{-1}}\).

A mass \(m_i\) of ice at \(0\,{}^\circ\mathrm{C}\) is added to mass \(m_w\) of water at \(T_i>0\,{}^\circ\mathrm{C}\). Derive the condition for all the ice to melt, assuming no heat exchange with the container or surroundings.

A hot metal of mass \(m_m\), heat capacity \(c_m\), and initial temperature \(T_m>100\,{}^\circ\mathrm{C}\) is placed in water of mass \(m_w\) initially at \(100\,{}^\circ\mathrm{C}\) in a sealed insulated vessel. Derive the mass of water that vaporizes if the final state remains at \(100\,{}^\circ\mathrm{C}\).