What is the formula of the energy required to change the temperature?

Question

BlackTom AI · Accepted Answer

To determine the energy required to change the temperature, we examine each option in turn. 
Option a: Q = Δm c T. This mixes up the variables: Δm would imply a change in mass, which is not what we’re calculating when heating a substance at a given mass. Also the arrangement c T is unconventional; the standard formula uses either ΔT or T in the appropriate positions, not a product with T alone. So this is not correct.
Option b: Q = m c ΔT. Here Q is the heat energy required, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature (final minus initial). This exactly matches the well-known calorimetry relation Q = m c ΔT, which calculates the energy needed to raise (or lower) the temperature of a mass m by ΔT units, given its specific heat capacity c. This is the correct formulation for temperature change.
Option c: Q = Δm C T. This resembles a mishmashed version: Δm would denote a change in mass, C is typically used as specific heat in some contexts but here it’s uppercase and combined with T without a Δ, which makes the units and meaning inconsistent with the standard heat equation. It doesn’t correctly represent the energy needed for heating.
Option d: Q = m C ΔT. This is nearly identical to option b but uses an uppercase C instead of c; if C is intended to be the same as c (specific heat), this is effectively the same as option b and would be correct only if C and c are interchangeable in the given context. However, since the standard notation uses c, and the option uses C, this could be a trick depending on case sensitivity. Given typical conventions, it is safer to treat c and C as the same physical quantity, but the phrasing suggests potential mismatch, making this option ambiguous and not the preferred correct choice in a strict multiple-choice setting.
In summary, the most clearly correct, standard form for the energy required to change the temperature is Q = m c ΔT, which corresponds to option b.

UCIC 202503 PHYS101 Quiz 6

What is the formula of the energy required to change the temperature?

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