Question

Assume that the kinetic energy of a 1500kg  car moving at 135km/h  could be converted entirely into heat.

            What amount of water could be heated from 22?C to 55?C by the car's energy?         

Express your answer using two significant figures.

Answer 1

KE = 1/2mv^2

First, convert km/h to m/s.

135 km/h x (1000 m / 1 km) x (1 hour / 3600 seconds) = 37.5 m/s

Now use the KE equation

KE = (1/2)(1500 kg)(37.5 m/s)^2

KE = 1.05 * 10^6 Joules

Now use the energy in the equation q = mcdeltaT

1.05 * 10^6 J = m(4.18 J/g-C)(55 C - 22 C)

m = 7.6 * 10^3 grams

Answer 2

KE= 0.5mv^2. remember for this to be in joules m and v must be in metres per second and kg. so 135 km/h = 110/3.6 = 37.5 ms^-1 .

substituting into the equation,

we get KE = 1054687.5 J.

Thermal energy = MC(T2-T1) J ...where, M = mass of water in grams, C = 4.2 (specific heat capacity).

Kinetic Energy = Thermal Energy

therefore, mass M = Kinetict Energy/ (temp change x 4.2) = 1054687.5/(33 x 4.2) = 7609.58 g = 7.61 kg.