Question

A washing machine heats 10kg of water in each wash cycle. How much energy is saved by washing at 30'c instead of 50'c if the starting temperature of the cold water is 16'c? The specific heat capacity of water is 4200 J/Kg'c

Answer 1

`8.4 * 10^(5)\; \rm J`, assuming that there's no heat exchange between the washing machine and the environment.

Step-by-step explanation:

Let
`m` denote the mass of water and
`c` the specific heat capacity of water. The energy required to raise the temperature of that much water by
`\Delta T` would be:

`Q = c \cdot m \cdot \Delta T`.

Washing at
`30\; \rm ^(\circ) C` would require a temperature change of
`\Delta T = 30\; \rm ^(\circ) C - 16\; ^(\circ) \rm C = 14\; \rm K`.

Washing at
`50\; \rm ^(\circ) C` would require a temperature change of
`\Delta T = 50\; \rm ^(\circ) C - 16\; ^(\circ) \rm C = 34\; \rm K`.

In both situations,
`c = 4.2 * 10^(3)\; \rm J \cdot kg \cdot K^(-1)` while
`m = 10\; \rm kg`.

Calculate the energy required in either situation:

Washing at
`30\; \rm ^(\circ) C`:

`\begin{aligned}& Q({30\; ^(\circ) {\rm C}}) \\ &= c \cdot m \cdot \Delta T \\ &= 4.2 * 10^(3)\; \rm J \cdot kg \cdot K^(-1) * 10\; \rm kg * 14\; \rm K \\ &= 588000 * 10^(5)\; \rm J\end{aligned}`.

Washing at
`50\; ^(\circ) {\rm C}`:

`\begin{aligned}& Q({50\; ^(\circ) {\rm C}}) \\ &= c \cdot m \cdot \Delta T \\ &= 4.2 * 10^(3)\; \rm J \cdot kg \cdot K^(-1) * 10\; \rm kg * 34\; \rm K \\ &= 1428000 \; \rm J\end{aligned}`.

`1428000\; \rm J - 588000\; \rm J = 8.4 * 10^(5)\; \rm J`.