A typical woman gives off heat at the rate of about 8000 calories per hour. How long would a woman have to stay in a bath of 60L (60,000g)of 26*C water in order to raise the water temperature to 30*C. Presume that all the heat given off by the woman is transferred to the water, and that the water doesn't lose any heat to the air.
To answer this question, we need to calculate the amount of heat required to raise the temperature of the bathwater and compare it to the heat output of the woman.
First, let's calculate the heat required to raise the temperature of the bathwater from 26°C to 30°C using the specific heat formula:
Q = m * c * ΔT
where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Given that the mass of the water is 60,000g (or 60kg), the specific heat capacity of water is 1 calorie/gram °C, and ΔT is 30°C - 26°C = 4°C, we can plug in these values and calculate the heat required:
Q = 60,000g * 1 calorie/gram °C * 4°C
Q = 240,000 calories
Q = 240 kcal
Next, let's calculate the amount of heat the woman gives off in one hour:
Heat given off = 8000 calories/hour
Now, we can determine how long she would need to stay in the bath for the transferred heat to match the heat required to raise the temperature of the water:
Time = Heat required / Heat given off
Time = 240 kcal / 8000 calories/hour
Time = 0.03 hours or 1.8 minutes
Therefore, a woman would need to stay in the bath for approximately 1.8 minutes to raise the water temperature from 26°C to 30°C, assuming that all the heat given off by the woman is transferred to the water and no heat is lost to the air.