Calorimetry And Heat Exchange

Question

A 200 g copper block at 100 °C is dropped into 300 g of water at 20 °C inside an insulated cup. Given copper's specific heat is $0.39	ext{ J g}^{-1}	ext{K}^{-1}$ and water's is $4.18	ext{ J g}^{-1}	ext{K}^{-1}$, find the equilibrium temperature.

RankGuru · Accepted Answer

When two bodies are mixed in an insulated container, the principle of calorimetry requires that heat lost by the hotter body equals heat gained by the cooler one, since no energy escapes. Let $T$ be the common final temperature. Heat lost by copper is $m_c c_c (100 - T)$ and heat gained by water is $m_w c_w (T - 20)$. Setting them equal: $200(0.39)(100 - T) = 300(4.18)(T - 20)$, which is $78(100 - T) = 1254(T - 20)$. Expanding gives $7800 - 78T = 1254T - 25080$, so $32880 = 1332T$ and $T \approx 24.4\,°	ext{C}$. The value 30 °C ignores the large heat capacity of water. The value 60 °C wrongly takes the simple average of the two temperatures. The value 21.5 °C overweights the water and underestimates copper's contribution. This balance assumes the cup is perfectly insulated and that no heat is absorbed by the container itself, so all the energy lost by copper is accounted for by the water. As a plausibility check, water has both more mass and a far higher specific heat than copper, so the equilibrium temperature should lie close to water's initial 20 °C, and 24.4 °C is appropriately near it rather than near the midpoint of the two starting temperatures.

Calorimetry And Heat Exchange

Select the correct option:

🔒 Solution Hidden from View

More thermodynamics Practice Questions

For a diatomic ideal gas the molar specific heat at constant volume is 5R/2, so what is the value of...

A gas is taken around a complete thermodynamic cycle and returns to its original state after several...

Two moles of an ideal gas expand isothermally at 300 K from a volume V to a volume 2V in a slow reve...

A balloon suddenly bursts and the compressed gas inside rushes out into the open atmosphere very rap...

When 2 moles of a monatomic ideal gas are heated at constant pressure causing a temperature rise of ...

On a pressure-volume diagram an isothermal curve and an adiabatic curve pass through the same point ...

A heat pump uses 200 J of work to deliver a total of 800 J of heat into a warm room during each oper...

Two identical samples of the same ideal gas are kept at the same temperature but stored at very diff...

One mole of an ideal gas is compressed isothermally at temperature 300 K, so what happens to its int...

Heat of 400 J is supplied to a gas sealed inside a rigid steel container whose volume cannot change,...

An ideal gas expands at a constant pressure of 2 × 10^5 Pa, increasing its volume from 0.01 m^3 to 0...

A gas confined in a perfectly insulated cylinder is suddenly compressed by a fast-moving piston, so ...

About This Question

Solution