Chapter 12, Problem 046 A piece of glass has a temperature of 80.0 °C. Liquid th

Question

Chapter 12, Problem 046 A piece of glass has a temperature of 80.0 °C. Liquid that has a temperature of 32.0 °C is poured over the glass, completely covering it, and the temperature at equilibrium is 58.0 °C. The mass of the glass and the liquid is the same. Ignoring the container that holds the glass and liquid and assuming that the heat lost to or gained from the surroundings is negligible, determine the specific heat capacity of the liquid. Number Units the tolerance is +/-390 Click if you would like to Show Work for this question: Open Show Work SHOW HINT LINK TO TEXTLINK TO TEXT By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set hy vour instructor

Explanation / Answer

Let the mass of the glass and liquid be m

Let the temperature of the glass is t1 = 80.0° C

Let the temperature of the unknown liquid is t2 = 32°C

Equilibrium temperature be T = 58°C

Specific heat of the glass is C1 = 0.20 cal/g C

Let the specific heat of the liquid be C2

If two masses m1 and m2 at temperatures t1 and t2 having specific heats C1 and C2 are mixed , then the equilibrium temperature is given by

T = ( m1 * C1 * t1 + m2 * C2 * t2 ) / ( m1 C1 + m2 C2 )

Here m1 = m2 = m , then

T = ( C1 t1 + C2 t2 ) / ( C1 + C2 )

58 = ( 0.2 × 80 + 32 C2 ) / ( 0.2 + C2 )

58 × ( 0.2 + C2 ) = ( 16 + 32 C2 )

11.6 + 58 C2 = 16 + 32 C2

58 C2 - 32 C2 = 16 - 11.6

26 C2 = 4.4

C2 = 4.4 / 26

C2 = 0.169 cal/g C

Note : C2 = 0.169 cal/ g C = 0.707 J/ g C = 707 J/kgK

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