The time it takes for cold water to reach room temperature depends on various factors, including the initial temperature of the water, the room temperature, and the volume of water. The larger the volume of water, the longer it generally takes to equilibrate with the surrounding temperature. The surface area of the container holding the water can also affect the rate of heat transfer.
It is important to note that the process by which heat transfer occurs is known as conduction. Conduction is the transfer of heat between objects in direct contact with each other. The rate of heat transfer depends on the temperature difference between the objects and the thermal conductivity of the materials involved.
As a rough estimate, assuming a typical room temperature of around 20 degrees Celsius (68 degrees Fahrenheit), and starting with cold water at approximately 4 degrees Celsius (39 degrees Fahrenheit), it might take anywhere from several minutes to an hour or more for a glass of water to reach room temperature. However, this can vary significantly depending on the size of the glass, the specific conditions, and other factors.
In the case of a bathtub, which contains a much larger volume of water, it would take considerably longer for the water to reach room temperature. It could take several hours or even overnight for a bathtub filled with cold water to equilibrate with the surrounding room temperature.
Factors such as insulation, air circulation, and the initial temperature of the room can also influence the rate of heat transfer and, therefore, affect the time it takes for the water to reach room temperature.
Keep in mind that these are general estimates, and actual times may vary based on specific conditions and variables involved.