A perfectly insulated cup is filled with water initially at 20C. Heat energy is transferred to the cup by an immersion heater at a steady rate. Sketch on the axes that follow the temp as a function of time. Explain the shape of your graph and write down a mathematical relationship for the temperature as a function of the quantity of heat energy (Q) that has been transferred to the water.

Question

i have T=Q/mc, is this right?

Answer 1

(T-To) = Q/mc, but they are interested in temperature (T) vs time, not vs Q.

Power(P) = dQ/dt is a rate at which heat is added

P/(mc) is the slope of the T vs t curve, which will be a straight line ramping upwards.

T = To + (P/mc)*t