Specific heat capacity

ΔT = Q / (m * c)
ΔT = 450 J / (0.05 kg * 900 J/kg°C)
ΔT = 10°C

The rise in temperature is calculated by dividing the energy absorbed by the product of the mass and specific heat capacity. This relationship stems from the definition of specific heat capacity.

Heating a metal block increases the kinetic energy of its constituent particles (atoms or molecules). This increased kinetic energy corresponds to an increase in the block's internal energy. Temperature is a measure of the average kinetic energy of these particles. Therefore, an increase in internal energy, due to the increased kinetic energy of the particles, results in a rise in the block's temperature.

As the temperature of the copper block increases, the average kinetic energy of the copper atoms increases. This means the copper atoms vibrate more vigorously around their fixed positions in the lattice structure. The higher the temperature, the greater the average kinetic energy and the faster the vibrations.

As temperature increases, the average kinetic energy of the particles increases. This means the particles move faster (translational, rotational, or vibrational motion, depending on the state of matter). Temperature is a measure of the average kinetic energy of the particles.

Formula: ΔE = mcΔθ
Rearrange for Δθ: Δθ = ΔE / (mc)
Δθ = 10000 J / (0.5 kg * 900 J/(kg°C))
Δθ = 22.22 °C
Final temperature = Initial temperature + Δθ
Final temperature = 20°C + 22.22°C = 42.22°C
Answer: 42.22 °C

Experimental Setup:
1. Insulate the metal block to reduce heat loss.
2. Insert a heater and a thermometer into the block.
3. Record the initial temperature (θ₁).
4. Turn on the heater and record the voltage (V) and current (I).
5. After a measured time (t), record the final temperature (θ₂).

Measurements:
* Mass of the block (m) in kg
* Initial temperature (θ₁) in °C
* Final temperature (θ₂) in °C
* Voltage (V) in V
* Current (I) in A
* Time (t) in s

Calculation:
1. Electrical energy supplied = V × I × t
2. Heat gained by the block = mc(θ₂ - θ₁)
3. Equate the two: V × I × t = mc(θ₂ - θ₁)
4. Rearrange to find c: c = (V × I × t) / (m × (θ₂ - θ₁))

*Explanation: This method uses electrical energy, which can be accurately measured, to heat a known mass of the solid. By measuring the temperature rise and knowing the energy input, the specific heat capacity can be determined.*

Formula:
* Energy supplied (E) = Power (P) × Time (t)
* Energy absorbed (E) = mass (m) × specific heat capacity (c) × temperature change (Δθ)
* c = E / (m × Δθ)

Working:
1. Calculate the energy supplied by the heater: E = P × t = 50 W × 300 s = 15000 J
2. Calculate the temperature change: Δθ = 35 °C - 20 °C = 15 °C
3. Calculate the specific heat capacity: c = 15000 J / (0.25 kg × 15 °C) = 4000 J kg⁻¹ °C⁻¹

Answer:
The specific heat capacity of water calculated from this experiment is 4000 J kg⁻¹ °C⁻¹.

*Explanation: This calculation uses the energy supplied to the water to determine the amount of heat required to raise the temperature of 1kg of water by 1°C.*