When you take a bath, how many kg of hot water (49 C) must you mix with cold water (13 C) so that the temperature of the bath is 36 C? The total mass of the water (hot and cold) is 191 kg.

57, 109

To find out how many kilograms of hot water you need to mix with cold water, we can use the principle of heat transfer.

The formula for heat transfer is Q = mcΔT, where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

Let's denote the mass of hot water as x kg and the mass of cold water as (191 - x) kg.

Using the formula, we can set up the equation:

Q_hot + Q_cold = 0

Since no heat is lost or gained during the process:

m_hot * c * (T_hot - T_target) + m_cold * c * (T_cold - T_target) = 0

Now, let's substitute the given values:

x * c * (49 - 36) + (191 - x) * c * (13 - 36) = 0

13x - 12(191 - x) = 0

13x - 2292 + 12x = 0

25x = 2292

x = 91.68 kg

So, you need to mix approximately 91.68 kg of hot water with the remaining cold water to achieve a temperature of 36 °C in the bath.