A 12-kg steel bar [with specific heat capacity of 452 J/(kg...

A 12-kg steel bar [with specific heat capacity of 452 J/(kg · °C)] heated to 1000 °C is immersed into 2 L of liquid mercury at an ambient temperature of 20 °C. Given that mercury has a density of 13.5 kg/L, a specific heat capacity of 140 J /(kg · °C), a latent heat of vaporization of 295 kJ/kg, and a boiling point of 357 °C, how much of the mercury boils off (i.e. is converted into mercury vapour)? 2 kg 27 kg 7.5 kg 11.5 kg 12 kg

Transcript

00:01 Hello students, in this question given that the mass of steel bar that is m steel which is equal to 12 kilogram and specific heat capacity of the steel which is equal to 452 joule per kilogram per degree celsius and the initial temperature that is ti is 1000 degree celsius and the ambient temperature is 20 degree celsius, volume of mercury is 2 liters, density of mercury is 13 .5 kilogram per liter and the specific heat capacity of mercury is 140 joule per kilogram degree celsius, latent heat of vaporization l is 295 kilo joule per kilogram and the boiling point of mercury is 357 degree celsius.

01:05 Now let's proceed with the calculations.

01:08 First let's calculate the heat transfer to the mercury which is equal to q is equal to mass of steel specific heat capacity of the steel into delta t.

01:17 Now let's substitute the values which is 12 into 452 multiplied by delta t is 1000 minus 20 degree celsius and this is equal to 5227440 joules.

01:32 Now let's calculate the temperature change of mercury and this is equal to qmc mercury into delta t of mercury.

01:42 Here we have to calculate the temperature change of mercury that is delta t of m.

01:47 This is equal to q by m into divided by cm and sorry this is q divided by mcm.

01:58 So now first let's calculate the mass of mercury.

02:02 So mass of mercury equal to density of mercury multiplied by the volume of mercury.

02:06 Here the density of mercury is 13 .5 kilogram per liter multiplied by volume is 2 liter.

02:14 So this gives 27 kilogram.

02:17 Now let's substitute the value of mass of mercury here so that the change in temperature of mercury is 5227440 divided by mass here is 27 kilogram multiplied by 140.

02:33 So therefore we get the temperature change of mercury is 129 degree celsius.

02:39 This is an approximate value.

02:41 And now we have to determine the amount of mercury that reaches the boiling point...

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