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A body cools in a surrounding which is at a constant temperature of ${\theta _0}$. Assume that it obeys Newton's law of cooling. Its temperature $\theta $ is plotted against time $t$ . Tangents are drawn to the curve at the points $P(\theta = {\theta _1})$ and $Q(\theta = {\theta _2})$. These tangents meet the time axis at angles of ${\varphi _2}$and ${\varphi _1}$, as shown
If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q? ( $\sigma$ stands for Stefan's constant.)
The radiation energy density per unit wavelength at a temperature $T$ has a maximum at a wavelength $\lambda _0$. At temperature $2T$, it will have a maximum at a wavelength
An object is cooled from $75°C$ to $65°C$ in $2$ minutes in a room at $30°C$ . The time taken to cool another object from $55°C$ to $45°C$ in the same room in minutes is
Two spherical bodies $\mathrm{A}$ (radius $6 \mathrm{~cm}$ ) and $\mathrm{B}$ (radius $18 \mathrm{~cm}$ ) are at temperature $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively. The maximum intensity in the emission spectrum of $\mathrm{A}$ is at $500 \mathrm{~nm}$ and in that of $\mathrm{B}$ is at $1500 \mathrm{~nm}$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$ ?
Figure shows three different arrangements of materials $1, 2$ and $3$ to form a wall. Thermal conductivities are $k_1 > k_2 > k_3$ . The left side of the wall is $20\,^oC$ higher than the right side. Temperature difference $\Delta T$ across the material $1$ has following relation in three cases