Water with a mass of m = 2 kg, which is at t1 = 15 ° C, heats up. Find the final t of water (t2), if the same amount of energy

Water with a mass of m = 2 kg, which is at t1 = 15 ° C, heats up. Find the final t of water (t2), if the same amount of energy is used to heat water as a body m1 = 5 kg, moving with a speed v = 72 km / h

mw = 2 kg.

C = 4200 J / kg * ° C.

t1 = 15 ° C.

m = 5 kg.

V = 72 km / h = 20 m / s.

Ek = Q.

t2 -?

The amount of thermal energy Q, which is necessary for heating water, is expressed by the formula: Q = C * mw * (t2 – t1), where C is the specific heat capacity of water, mw is the mass of heated water, t2, t1 are the final and initial water temperatures.

The kinetic energy of the body Ek is determined by the formula: Ek = m * V2 / 2, where m is the mass of the body that moves, V is the speed of the body.

As Ek = Q, then m * V ^ 2/2 = C * mv * (t ^ 2 – t1).

m * V ^ 2/2 = C * mb * t ^ 2 – C * mb * t1.

C * mb * t ^ 2 = m * V ^ 2/2 + C * mb * t1.

t2 = m * V ^ 2/2 * C * mv + t1.

t2 = 5 kg * (20 m / s) ^ 2/2 * 4200 J / kg * ° C * 2 kg + 15 ° C = 15.1 ° C.

Answer: the final water temperature will be t2 = 15.1 ° C.