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When you’re presented with a problem that asks for the final temperature of a substance after a heat transfer—such as heating water from a given starting temperature—you can determine the answer using the classic thermodynamic relation for specific heat.
Thermodynamics, the branch of physical science that describes the flow of heat and energy, provides a straightforward equation that links the heat added or removed (Q), the mass of the substance (m), its specific heat capacity (c), and the resulting temperature change (ΔT).
The basic specific‑heat relationship is
Q = mcΔT
Here, Q is the heat exchanged (in calories or joules), m is the mass (grams), c is the specific heat capacity (cal g⁻¹ °C⁻¹ or J kg⁻¹ K⁻¹), and ΔT is the temperature change (°C or K). Solving for ΔT gives
ΔT = Q / (m c)
Divide both sides of the original equation by mc to isolate ΔT.
Suppose the problem states that 150 cal of heat are added to 25.0 g of water. Water’s specific heat capacity is 1.0 cal g⁻¹ °C⁻¹. Plugging these numbers into the formula:
ΔT = 150 cal ÷ (25.0 g × 1.0 cal g⁻¹ °C⁻¹) = 150 ÷ 25.0 = 6.0 °C
The water’s temperature rises by 6.0 °C.
Add the temperature change to the initial temperature. If the water started at 24 °C, the final temperature is
24 °C + 6.0 °C = 30.0 °C
Thus, after receiving 150 cal of heat, the water reaches 30 °C.
