Question

When 47.1 J of heat is added to 14.0 g of a liquid, its temperature rises by 1.80 ∘C. What is the heat capacity of the liquid?

Answer 1

`\boxed {\boxed {\sf 1.87 \J/g \textdegree C}}`

Step-by-step explanation:

We are asked to find the specific heat capacity of a liquid. We are given the heat added, the mass, and the change in temperature, so we will use the following formula.

`q= mc\Delta T`

The heat added (q) is 47.1 Joules. The mass (m) of the liquid is 14.0 grams. The specific heat (c) is unknown. The change in temperature (ΔT) is 1.80 °C.

• q= 47.1 J
• m= 14.0 g
• ΔT= 1.80 °C

Substitute these values into the formula.

`47.1 \ J = (14.0 \ g) * c * (1.80 \textdegree C)`

Multiply the 2 numbers in parentheses on the right side of the equation.

`47.1 \ J = (14.0 \ g * 1.80 \textdegree C)*c`

`47.1 \ J = (25.2 \ g*\textdegree C) *c`

We are solving for the heat capacity of the liquid, so we must isolate the variable c. It is being multiplied by 25.2 grams * degrees Celsius. The inverse operation of multiplication is division, so we divide both sides of the equation by (25.2 g * °C).

`\frac {47.1 \ J}{(25.2 g *\textdegree C)} = \frac {(25.2 g *\textdegree C)*c}{{(25.2 g *\textdegree C)}}`

`\frac {47.1 \ J}{(25.2 g *\textdegree C)} =c`

`1.869047619 \ J/g *\textdegree C = c`

The original measurements of heat, mass, and temperature all have 3 significant figures, so our answer must have the same. For the number we found that is the hundredth place. The 9 in the thousandth place to the right tells us to round the 6 up to a 7.

`1.87 \ J/ g * \textdegree C =c`

The heat capacity of the liquid is approximately 1.87 J/g°C.