A cup of tea cools from $80^{\circ} C$ to $60^{\circ} C$ in one minute. The ambient temperature is $30^{\circ} C$. In cooling from $60^{\circ} C$ to $50^{\circ} C$. It will take:
- 50 sec
- 90 sec
- 60 sec
- 48 sec
The Correct Option is D
Solution and Explanation
$\frac{80^{\circ}-60^{\circ}}{60^{\circ}}=K\left(\frac{80^{\circ}+60^{\circ}}{2}-30^{\circ}\right) $
$\frac{1}{3}=K(4)\,\,\,\,...(1) $
$\frac{60^{\circ}-50^{\circ}}{t}= K \left(\frac{60^{\circ}+50^{\circ}}{2}-30^{\circ}\right)$
$\frac{10}{t}=K(25)\,\,\,\,...(2)$
Dividing equation (1) by (2), we get
$\frac{t}{30}=\frac{40}{25}$
or $t=\frac{40}{25} \times 30$
$=48\, \sec$
Top Questions on thermal properties of matter
- Match List-I with the List-IIChoose the correct answer from the options given below:
List-I
(Molecule / Species)List-II
(Property / Shape)(A) \(SO_2Cl_2\) (I) Paramagnetic (B) NO (II) Diamagnetic (C) \(NO^{-}_{2}\) (III) Tetrahedral (D) \(I^{-}_{3}\) (IV) Linear - JEE Main - 2024
- Chemistry
- thermal properties of matter
- An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a – 2b), the value of tension will be_____ N.
- JEE Main - 2024
- Physics
- thermal properties of matter
- The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are \( 8 \, \Omega \) and \( 10 \, \Omega \) respectively. After inserting in a hot bath of temperature \( 400^\circ \text{C} \), the resistance of the platinum wire is:
- JEE Main - 2024
- Physics
- thermal properties of matter
- Two persons pull a wire towards themselves. Each person exerts a force of $200 \, \text{N}$ on the wire. Young’s modulus of the material of the wire is $1 \times 10^{11} \, \text{N m}^{-2}$. Original length of the wire is $2 \, \text{m}$ and the area of cross-section is $2 \, \text{cm}^2$. The wire will extend in length by ______ $\mu \text{m}$.
- JEE Main - 2024
- Physics
- thermal properties of matter
- A lead bullet penetrates into a solid object and melts . Assuming that 40 % of its kinetic energy is used to heat it , the initial speed of bullet is :
(Given ,initial temperature of the bullet =127∘C)
Latenet heat of fusion of lead = 2.5×104 J kg−1,
Specific heat capacity of lead = 125 J/KgK)- KEAM - 2023
- Physics
- thermal properties of matter
Questions Asked in JIPMER exam
- Binomial nomenclature was first introduced by
- JIPMER - 2015
- KCET - 2022
- Diversity In The Living World
- A convex lens $'A'$ of focal length $20\, cm$ and a concave lens $'B'$ of focal length $5\, cm$ are kept along the same axis with a distance $'d'$ between them. If a parallel beam of light falling on $'A'$ leaves $'B'$ as a parallel beam, then the distance $'d'$ in cm will be :
- JIPMER - 2021
- Spherical Mirrors
- A bacterial flagellum is composed of
- JIPMER - 2021
- Prokaryotic Cells
- $2,4-DNP $ test can be used to identify :
- JIPMER - 2021
- Chemical Reactions
- How many moles of acidified $K_2Cr_2O_7$ is required to liberate $6$ moles of $I_2$ from an aqueous solution of $I^-$ ?
- JIPMER - 2020
- Mole concept and Molar Masses
Concepts Used:
Thermal Properties of Matter
Anything that has mass or occupies space in the universe is commonly known as matter. There are five properties of matters namely chemical, mechanical, thermal, dimensional, and physical properties.
Read More: Thermal Properties of Matter
Heat Capacity:
The quantity of heat needed to change the temperature of the matter by 1° is known as the heat capacity of a material. The temperature is indicated in kelvin or Celsius and the amount of heat is shown in calories or joules. Specific heat capacity or molar heat capacity is used to calculate the heat capacity of the matter with the stated dimension.
Linear expansion is the situation when change takes place in one dimension or dimensional.
Thermal Expansion:
When heat is passed through the material, the change in the area, volume, and shape is recognized as the thermal expansion property of the material. The expansion of the railway tracks due to maximal heat which leads to accidents is an example of thermal expansion.
Thermal Conductivity:
This property is interconnected to the conductivity of heat. The amount of heat regulated by the material is directly proportional to the conductivity of the material. Not all objects have the capacity to conduct heat throughout their bodies. Insulators are such objects which do not have the property to conduct heat throughout their body.
Thermal Stress:
The stress due to thermal contraction or expansion of the body is known as thermal stress. The explosion of materials takes place due to thermal stress which is dangerous. The cracks on the truck tyres are caused by an outcome of thermal stress. Trucks at high speed generate heat which is caused by the friction of the truck tyres and the road surface.