Question

1. how much heat does it take to raise the temperature of ten - kilograms of water by one degree celsius?
2. how much thermal energy would it take to heat one kilogram of water by ten degrees celsius?
3. how much thermal energy would it take to change the temperature of two kilograms of aluminum by three degrees celsius?

Explanation:

Step1: Recall heat transfer formula

The formula for heat energy is $Q = mc\Delta T$, where:

• $Q$ = thermal energy (in joules),
• $m$ = mass (in kg),
• $c$ = specific heat capacity: $c_{\text{water}} = 4180\ \text{J/(kg·°C)}$, $c_{\text{aluminum}} = 900\ \text{J/(kg·°C)}$,
• $\Delta T$ = temperature change (in °C).

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For Question 7:

Step1: Define given values

$m = 10\ \text{kg}$, $c_{\text{water}} = 4180\ \text{J/(kg·°C)}$, $\Delta T = 1\ \text{°C}$

Step2: Substitute into formula

$Q = 10 \times 4180 \times 1$

Step3: Calculate result

$Q = 41800\ \text{J}$

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For Question 8:

Step1: Define given values

$m = 1\ \text{kg}$, $c_{\text{water}} = 4180\ \text{J/(kg·°C)}$, $\Delta T = 10\ \text{°C}$

Step2: Substitute into formula

$Q = 1 \times 4180 \times 10$

Step3: Calculate result

$Q = 41800\ \text{J}$

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For Question 9:

Step1: Define given values

$m = 2\ \text{kg}$, $c_{\text{aluminum}} = 900\ \text{J/(kg·°C)}$, $\Delta T = 3\ \text{°C}$

Step2: Substitute into formula

$Q = 2 \times 900 \times 3$

Step3: Calculate result

$Q = 5400\ \text{J}$

Answer:

1. $41800\ \text{joules}$
2. $41800\ \text{joules}$
3. $5400\ \text{joules}$