How much there will be temperature of the resultant water, if we add cold water into hot water.

Hello friends,

Today we will discuss about heat and some interesting phenomenon happened due to heat. And we also discuss about our topic which is “how much there will be temperature of the resultant liquid (water), if we add cold water into hot water.”

Before we start we must understand heat and temperature. to know what is heat and temperature and what is difference between heat and temperature,

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NOW let’s start our topic

We will find the answer of the question, when both liquid are same (i.e. both are water). and we also know what will be temperature of the resultant liquid, when both liquid are different.

Let’s take a question and try youself.

Q). 100 g of water at 10 ℃ is mixed with 200 g of water at 70 ℃. what will be final temperature of the mixture?

The branch of physics which deals with measurement of heat is called Calorimetry. And the device which is used to measure heat is called calorimeter.

The principal of calorimeter or heat balance states that

HEAT LOSS=HEAT GAIN

That means the amount of heat loosed by a system is equal to the heat gained by other system. The system whose temperature is more than its surrounding loses heat and surrounding gains the heat lost by the system.

Heat always flows from hot body (high temperature) to cold body (low temperature)

Consider a system A of mass m₁, specific heat C₁ and temperature T₁ .

let and another system B whose mass is m₂, specific heat C₂ and temperature T₂ is brought in contact of system a.

If temperature of system A (T₁) > temperature of system B (T₂)

Then heat will be flow from system A to system B till these two system are in thermal equilibrium at temperature T ,mean heat will be flow from system A to system B till these two system not having same temperature T.

i.e. final temperature =T

now,

Heat loosed by system A = m₁C₁ (T₁-T)

Heat gained by system B = m₂C₂(T-T₂)

According to The principal of calorimeter

HEAT LOSS = HEAT GAIN

m₁C₁ (T₁-T) = m₂C₂(T-T₂)

Now you can able to find the temperature of resultant solution of two different liquid.

If both liquid are same then formula will be

m₁ (T₁-T) = m₂(T-T₂)

Here C1 and C2 will be same because specific heat of both system (liquid) are same. Know more about specific heat capacity at the end of this page.

Q). 100 g of water at 10 ℃ is mixed with 200 g of water at 70 ℃. what will be final temperature of the mixture?

In system A,

Mass of water= 200g

Temperature = 70 ℃

In system A,

Mass of water= 100g

Temperature = 10 ℃

Let final temperature =T

According to The principal of calorimeter

HEAT LOSS = HEAT GAIN

m₁C₁ (T₁-T) = m₂C₂(T-T₂)

Here C1 and C2 will be same because both liquid are same  and specific heat of both system are same.

∴  m₁ (T₁-T) = m₂(T-T₂)

   200 (70 - T) = 100 ( T – 10)

     2 (70 - T)  =  T – 10

     140 - 2T =T – 10

     3T = 150

     T = 50℃

Therefore, final temperature of the mixture=50℃
Important topic

………………………………………………………

What is specific heat?

Ans-Specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of 1g of substance through 1℃.

When a body is heated its temperature increases on the otherhand, temperature of body decreases when it is cooled it is found that the loss or gain of heat is directly proportional to

Q ∞ m (mass of the body)                 

Q ∞ ∆T(change in temperature of the body)

∴    Q ∞ m∆T

or,  Q=C m∆T

where C is proportionality constant and it is known as specific heat.

It depends on the nature of the material of the body.

 Thus , Heat transferred = mass of the body x specific heat x change in temperature

 If m=1g and ∆T=1℃

Then Q=C

Therefore, Specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of 1g of substance through 1℃.

 ∴ C=Q/ m∆T

• ·    SI unit of specific heat is J/kg K  ,
• ·    Dimensional formula [M⁰L²T^-2K^-1]
• ·    Table of specific heat capacity of various substance.

Substance	c in J/gm K
Aluminum	0.900
Copper	0.386
Gold	0.126
Silver	0.233
Tungsten	0.134
Zinc	0.387
Mercury	0.140
Alcohol(ethyl)	2.4
Water	4.186
Ice (-10 C)	2.05
Glass	.84

Thank you

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