Question

The specific heat capacity of liquid water is 4.18 J/g-K. How many joules of heat are needed to raise the temperature of 5.00 g of water from 15.0 °C to 36.5 °C?

Answer 1

The specific heat capacity of a substance is the amount of energy required to raise the temperature of 1g of the substance by 1K.

`\begin{gathered} q=mc\Delta T \\ q:energy\text{ }(J)=x \\ m:mass\text{ }(g)=5.00g \\ c:specific\text{ }heat\text{ }capacity\text{ }(Jg^(-1)K^(-1)) \\ \Delta T:change\text{ }in\text{ }temperature\text{ }(K) \\ \Delta T:(final\text{ }temperature-initial\text{ }temperature) \end{gathered}`

Calculating the change in temperature:

`\Delta T:(273.15K+36.5\degree C)-(273.15K+15\degree C)=21.5K`

By substituting what we are given into the equation to solve for the unknow x we have;

`\begin{gathered} q=5.00g*4.18Jg^(-1)K^(-1)*21.5K \\ q=+449.35J \end{gathered}`

Answer: Energy needed is 449.35J