Question

1. a glass cup that holds 8 ounces of liquid has a mass of 0.225 kg.

a. how much heat it would take to change the temperature of the glass by eight degrees celsius?
b. convert eight degrees celsius to kelvin.

1. the average human body has a mass sixty kilograms.

a. calculate how much thermal energy is needed to raise the temperature 0.5 °c for an average.
b. convert 0.5 °c to fahrenheit.

Explanation:

Step1: Recall heat formula for glass

The heat required is calculated using $Q = mc\Delta T$, where $m=0.225\ \text{kg}$, $c=840\ \text{J/(kg·°C)}$ (specific heat of glass), $\Delta T=8\ \text{°C}$.

Step2: Substitute values and solve

$Q = 0.225 \times 840 \times 8$
$Q = 0.225 \times 6720 = 1512\ \text{J}$

Step3: Convert °C to Kelvin

Use $K = °C + 273.15$, $\Delta T_K = 8 + 273.15$

Step4: Recall heat formula for human body

Use $Q = mc\Delta T$, where $m=60\ \text{kg}$, $c=3500\ \text{J/(kg·°C)}$ (specific heat of human body), $\Delta T=0.5\ \text{°C}$.

Step5: Substitute values and solve

$Q = 60 \times 3500 \times 0.5$
$Q = 60 \times 1750 = 105000\ \text{J} = 1.05 \times 10^5\ \text{J}$

Step6: Convert °C to Fahrenheit

Use $°F = (°C \times \frac{9}{5}) + 32$, $°F = (0.5 \times \frac{9}{5}) + 32$
$°F = 0.9 + 32 = 32.9$

Answer:

10a. $1512\ \text{J}$
10b. $281.15\ \text{K}$
11a. $1.05 \times 10^5\ \text{J}$
11b. $32.9\ \text{°F}$